C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

140

Transcript of C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

Page 1: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

� �������� �� � � ��� ����� ���

� ����������� "! ���#!%$&�'�)(*�+!,.-&/103254687 039:032<;:0>=?0A@B/34CEDGF

H�IKJMLONPL�Q�R+SUTONPV+WYXZR\[]R^JMIZL`_1I

Page 2: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...
Page 3: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

a�bdcfe?b8gAh?cie?b�jkh)glbmcie?gUnlopcfq.okbOr3e?qdc.osbktvuwexrlqdy{z|osq.exosb:}lg3e*jsh)u~osjsjky��h)g�nAo]rlqdh)�lu~o��zUe?bs��u{e�bdos�)}Agln3e�jkh)g�cfy{okglo%b.}lb]b.h)u~}ljsy~h)glosbk�3��uwe�cfosqdjsokqfeA����}lo�r�hZnAq��� e�okg�c.osglnAosq.bdojkh)zUhU}lg'e?r8�okglnly~jso?�^osb�}lg<q.osbd}lz|osg�nlo�u~h)b]c.oszUe?b�nAo�cfokh)q��� eA�]�BhKn3e?bxoku{uwe1b]okbdc��e1ge?bdhZjkywe?nle?b*e?u�js}Aq.b.h�nlo|j`�e?u~js}lu~h�gK}Az\�okq.y{jkh�y~zUrle?qdc.y{nlh�okg"�?��nlo��<e1c.osz��e1cfy~j�e?b�nlou{e��5��� oku8rlqdy{z|osq%b.okzUokbdcfqdo�nloku�e� glh�e?jse?n8�osz|y{jkh�¡?¢?¢A£¥¤)¡?¢?¢�¡Z��a�g>nly~ji¦lh#jk}lq.bdhbdo|bdy{�)}Ay{osqdh)g�uwe1b�glh?cie1b%nAoU§8�©¨x}ly{ql�h)b�cfyªcf}lu{e?n3e?b�«f¬��e?u{jk}lu{h�­5}lz\�osq.y~jsh�®.®E¯A�`nlo�uwe?bjk}3e?u{okbvb.opc.h)z�e1g°�?b.e?u~±?h%r�os��}lo� glh)b�j�e1z��ly{h?bs�)u{e�nly~±Ky~b.y��h?g�osg�b.okjsjky{h)glokb���j�e1r`�� c.}lu{h)bk�²`h)b�osg�}lgAjsywe1nlh)b�nlo�u{h?bxrlq.h?�lu{okz�e?b]b.h)g'okg³bd}´zUe��)h)qs�� e�h?q.y{�?y{g3e?u~osbk�^jkh)g'jsy{okqm�cfe?b*o�µZjsokr^jky{h)glokbs��¶:e1q.y{h?b�¦3e?g´b.y{nAh�c.h)zUe?nlh)b*nlo�¦lhM·.e1b�nlo�rlqdh)�lu~oszUe?b�nlosuOjk}lq.bdhe?g�c.osq.y~h)qs¸^e?u~�)}lglh)b]nlosuBu{y~�lq.h|nlo�ap�^¹�e?y~q.okqs�Pº^�¼»B�P­5½)q.bdokcdcx�<¾���¿>e1glglosq�«fºZh)uª±Ky{gl�h)qdnly{gle?qd�Unly~À^osqdosg�cfy{e?u�os��}3e1c.y{h)glb�£?�O­]h)glbmcfyªÀ#rlqdh)�lu{okzUbd¯l�Ajse?b.yPb.y{okzUrAq.oxjkh)g�zUhKnZ�yªÁ3j�e?jky{h)gAosbs¸°��}lglh�nlokuÂc.o�µKcfh�nlo|¬��°��h)q.okglh�¾*h?glÃ`�e?u~osÃ'«.¬��e?u{jk}lu{h�­]}lz\�osqdy{jsh�®d®E¯l�¬�}3e1glnlh#bdo�e<r�h)b.y~�lu{o1�Âbdo�jky~cie1q3�e�u{e�ÄÅ}Aosg�cfo�okg>uwe�b.h?u{}ljky��h)g°�ÇÆxo�cfhKn3e?b*ÄÅh)q.zUe?b%uweh)qdy{�)y~g3e?u~y{n3e?n�nAoÈu{h)bBrlqdh)�lu{okz�e1bGnlok�^oÈokg�cfosgAnlosqdb.oÉosg�bdosg�cfy~nlh�uwe¥µAhA�1��ex��}lo�z�}lji¦lh)bokbdc��e1g>�3e?b.e?nlh)b�okgÊq.okb.}luªcie?nlh?b��ly~osg>jkh)glhKjsy{nAh)bs��²`h)b�oE·dosq.jky{jky{h)b�osbdc3�e?gÊb.o� g3e?uwe1nlh)bjkh)gËc.q.osb|g��}lz|osqdh)b�b.okr3e?qfe1nlh)b�r�h)q�rl}lg�c.h)bs��a�uÉrlqdy{z|osq.h��\okupb.os�?}lglnlh>y~glnly~j�e?goku5jse?r`�� cf}lu~h´��uwe'b.okjsjky��h)g�e´uwe'��}lo<r�osqmcfosgAosjsokg°�p��osuÉcfosqdjsokq.h"bd}+h)qdnlosg+nAosg�cfqdhnlo�uwe�u~y{bmcieA�<aOu8b��� z��^h?u{h<ÌÎÍ'rlqdosjkosnly~osglnlh'e1u{�)}lgAh)b�oE·dosq.jky{jky{h)b�y{glnly~j�e<��}lo�b.h)gÊnlog3eMcf}lq.e?u{okÃ�e�rlq3�e1jkcfy~j�e��'uwe�zUe��)h)q*r3e1qdcfo�nlo�u{e?bx±)okjsosb�q.os��}ly~osqdosg´osz|rlu{ose?q�}lg´h)qm�nlokg3e?nlh?qs��²©eUnAy~Á3jk}lu~cfe?n#nlo�e?u{�)}Aglh)b�rAq.h)�lu~oszUe?b5h�e?r3e?qmcie?nAh)b�okbdc��eUy{glnly~j�e?nleUjsh?gjky{osqmcfh�g��}lz|osqdh���cie?zUe� glh�nAo�e1bdcfokq.y~b.jsh?bs�:�]gÇrlq.h?�lu{okz�e�nlo�nAh)b5e?bdc.osq.y~b.jkh)bÉrl}losnAobdosqÉnly~Áljsy{uÏ�� bdy{z|h�y~gljsu~}lb.h�r3e?q.e�u{h)bpz|oзdh)qdosb5e?u~}lzUgAh)bÈnlo*uwe�jkuwe?bdo?�²©e%bdos�)}Agln3e�rle?qdc.o5y~gljsu~}A�)o5uwe1b�b.h)u~}ljsy~h)glosbOjkh)zUrAu{okcfe?b�nloÉcfhKnlh)bOu{h?b:rAq.h)�lu~oszUe?boѵAjkosrAc.h�nlo�u~h)bÉrlq3�e1jkcfy~jsh)bk��­5h�bdo�¦3e?g<q.ok±Ky~bfe?nlhUnlo�ÄÅh?q.zUe�cfe?g#o�µZ¦3e1}lbdc.y~±1eUjkh)zUhu~h)b�osg�}lgljkywe?nAh)bs�Âr^h)q�u~h�js}3e?uOglhÇosb%nlo|o�µKcfq.e� g3e?q���}lo|jsh)g�c.osgl��e1g"jsy~osqmcfhÇgx�}lzUokq.hnlo�okq.qfeMcie?bk��®EgAjsu{}Ab.h´r^hKnlqs�� e#¦3e?��osqdb.o�nlosbdu{y~Ã�e?nlh'okg�e?u~�È�}lgÊj�e1b.h´}lgËokq.qdh)q�osg�osurlu{e?g�cfose?zUy~osg�cfhA��¬�}3e?u~��}ly{okq|jkh)q.qdosjkjsy��h?g�b.okq3�e´�ly{okg�±?osgly~n3e³oÇy{gAjsh)qdr^h)q.e?n3e'osgËuwe?br�h)b.y~�lu{okbȱ)okq.b.y~h)glokb5ÄÅ}Ac.}lqfe1bs�²`h)bGqdosb^�}AzUokglosbvnAo8cfokh)qs�� eA�?jkh)z|h�b.o�rl}losnAoÈu{okosqGokg�b.}lbGrlq.y~zUokqfe?bBuÒ�� glo�e?bk�MÄÅ}Aosq.h?gjkh)gljsok�ly{nAh)bOjsh)z|h%e��K}lnle�e?u3okbdcf}Anly{h*r3e?q.e%oku3js}lqdb.h�nl}lqfe1g�c.oÉosu���}loÉb.o5osuwe1�^h)q.e?q.h?g°�Æxokr^okglnlosg\ÄÅ}lokqdcfokzUokg�cfo�nlo�uwe<±?osqdb.y��h?g�nAo�uwe?b�glh1cie?b�nlo�§8�O¨x}ly{ql�h)b���}lo�b.o�nly~bm�c.q.y{�A}A���hÊosg�cfqdo´u~h)b�e?u~}lzUgAh)bs��Óx��±Ky{e?zUokg�cfo'uwe?b�jsh)glbdy{nlokqfe?jky{h)gAosb�e?jkosq.jse�nAo�u{h)bqdos��}ly{bdy~c.h)b�z��� gly~zUh?b:h�nloxuwe1b8Ä1�h)qdz�}luwe1b8��}loxjkh)g�±Ky{osgAo�zUokzUh)qdy{Ãse?qs��glh�rA}losnlokg�b.osqb.e?j�e?nle?bGnloku�jsh)g�cfoѵKcfhxnlokuZjk}lq.bdh�r3e1qdcfy~js}lu{e?qBe?u���}lo�bdo�qdokÁ3okq.osgP�v�Âokgly{okglnlhxokg�jk}losgZ�

Page 4: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

cfe��K}Ao%oku^c.oszUe?q.y~h�nlo�osbmcie�e?bdy{�)g3eMcf}lq.e�b.}AÄÅqdo�jsh)g�cfy~g�}lh)bpj�e1z��ly{h?bs�le1}lgl��}lo*r3e?qdosjsoe?jkosqdj�e?qdb.o#r�h)q�Á3gÔe³jky{osqmcie?bUuÒ�� glo�e?b|�É�e?bdy{jse?bs�pu{e"e��K}ln3e>e?u5osbmcf}lnAy{h>��}lo#rA}losn3e1gqdosrlqdosb.okg�cie?q5osbmcfh)b5q.okbP�}lz|osglokb5okg�oku°ÄÅ}Acf}Aq.hl�lokb]z�}A��qdosuweMcfy~±1eA�»Ge1qfe�cfokq.z|y{g3e?qk�^¦le��#e?u{�?}lg3e?bxjk}losbmcfy~h)glosb�nAo�cfy{r�h�h)qd��e?gly~Ã�e1c.y~±?h���}lo�r^hKnlqs�� e?gqdosb.}Au~cie1qvnlopy{g�c.osqK�okb�r3e?q.exu{h)bv��}lopy~zUrle?qdcfe?g�z��e?b�e?nlokuwe?g�c.oÈosbmcie*e?b.y~�)g3e1c.}lqfeZ�v¬Èe?nlebdoszUe?g3e�¦�}l��h�js}le1cfqdh�¦lh)q.e?bxnlo%cfosh?q��� e��<jk}3e1c.q.h�nlo�rlq3�e?j�cfy~j�e?bk�Puwe1b´�}luªcfy{zUe?bpnlyª±Kyª�nly~n3e?b�okg´nAh)b�cf}lqdglh)bs�©nlo�z|hKnlh���}lo�j�e?n3e�e?u~}lz|glh��)osgAosqfe1u{z|osg�cfo�bl�h)u{h�e?bdy{bmc��� e�enlh?b%nAo|oku{u{e?bs��²©e�r3e?qdc.o�cfo`�h?q.y{jse�b.o�ok±1e?u~}É�h�jkh)g´}lg³oѵAe?zUokg´Álg3e?uÏ�`z|y{okg�cfqfe1b%��}lor3e1qfe�uwe�r3e?qmcfo*rlql�e?jkc.y{j�e1bpb.o%osb.r�osjky~Á3jse?q.h?g�nlh?b5c.qfe?�3e�·dh)bÉe|u~h�uwe?qd�)h�nlosu`jk}lq.bdhl�8²Bejse?u{yªÁ3j�e?jky��h)gÇÁ3g3e?uBb.o�jkh)z|rl}lb.h�okg�}lg'Õ)¢�Ö×nlo�u{eUr3e1qdcfo�cfo`�h?q.y{jseU��osg'}lg���¢�ÖØnlou{e�rlq3�e?j�cfy~j�eA���]nlosz��e?bÉb.o*o�µZy~�)y��h���}lo*ÄÅ}losq.e�e?rlq.h?�3e?n3e�j�e?nle�rle?qdc.o%r�h)qpbdosr3e?q.e?nlhl�

Page 5: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

a�uÉjs}lqdb.h"¬��e?u{jk}lu{h´­]}Az\�okq.y{jkh'®.®�nlokuÉe� glh³¡?¢)¢A£�¤)¡?¢)¢�¡<jkh)g�cf}A±?h"u~h)b�j�e?r°�� cf}lu~h)b�\bdosjsjky{h)gAosb���}loÇb.oÇy{gAnly{jse?g�e'jsh?g�c.y{g�}3e?jky��h)gP�+²©e?b�b.o� gle?uwe?nle?b�jsh)g+ÙÚglh"okbdc��e1gjk}l�ly{okqdcfe?bOr^h)q�u~h)b�rlqdh)�lu{okz�e1bs�²Be*rlqdy{z|osqfexr�h)qd�K}Ao5okbOnloÉj�e?ql�e?jkc.osqOrlq3�e1jkcfy~jshl�)��uwe?bh?c.qfe?bpr�h)qd�K}Ao%oku��}lu~c.y{z|h�jse?r`�� c.}lu{h�ÄÅ}Ao�zUy~gly{z|y{Ãse?nlh���b.o*jsh?glb.y~nlosq.e?q.h)gÇb.}ZÁ3jsy~osg�cfokbu~h)bpoзdokzUrlu~h)bpnlo*jsu{e?b.o1�

ÛUÜÞÝ ßàxáOâ<ã´â�äåã´à æ³ç è´é�ä�âê3ë*ìsí^î�ïMð°ñÂòBó�ó�ôKõð�íö°ë%÷øõù î�ð°ñBðÊñ ù#ú òBû ù ïü°ë%ýÇí�þÿõù î�ð`ñBð"ôYþ��Gûfõ� ó�ô î�ð��5û��'ï ù�� û��´ñ ù û:î�ï�� ù ó�ô ð�©ë%÷øõù î�ð°ñBð �|ñ ù�� ���`û ð�ï�°ë%÷øõù î�ð°ñBð �|ñ ù òBí������sð�°ë%÷øõù î�ð°ñBð �|ñ ù�� òÂí ��ù���� ò`î�î��� ë���ð�íBñÂô ó�ôÅð^í ù ��ñ ù ð�ïMñ ù í °ë õ! ï#"�ð�û ù �|ñ ù�$ ò`î¥ó#% ù ï&°ë(' ù þ"ð �kî�ï#�ló�ôKõð�í�ñ ù ûÅð ��î ù ð�ï ù þ)����ñ ù�$ ò©î�ó*% ù ïê�+`ë�÷ õù î�ð`ñ©ð � ù�, �Âûfõ� ó�ô î�ð �?ë.-�ïMñ ù í+ð "©î ù íBô�"Âû ùê�ê3ë ú �kî¥ô þ)�3ó�ôÅð^í ù ��ñ ù#ù ïMï¥ð�ïêKö°ë ú/, î�ï���ð�û��ló�ôKõð�í�ñ ù�� ô ó#%��lïMñ��sð�íêKü°ë0�.�3þ�"Âô ð"ñ ù �1��sðê��©ë(23�lï ù � ù íÂó4��56�3ñBð �Ù ê7�°ë.'�ô�� � ï�3þ)��|ñ ù#ù�8 ó�ô ù íBó�ô��9ÇÜ;:=< â?>A@sà.B é�ä äGáDC6Eê3ë�FHG|ò�õù#ù �UòBí��BïMðI"Âû ù þ)�J��î¥ôLK�Mö°ë('�ð�þ>ô íBô ð´ñ ù#ù �kî��"ÂôYû ô ñ��3ñ�ûYô í ù �3ûN�PO �.ù ��î��"ÂôYû ôYñ��3ñü°ë ú �kî��"Âô ûYô ñ��lñ�ñ ù þ õù î�ð`ñ©ð �|ñ ù�� òBí ��ù4��� ò`î�î��Q�Ü;R CTS�à < à�ç�UVCsé�äXW>ç�C�áOé�äê3ë(YZ�\[lõð�ïMþ´òBûL�³ñ ù ó�ô íÂó)ð\�ÂòÂí^î�ð]�^�Ü;_ @sà.B à�ç�áOâ�ä`W>ç\C�áOâ�äê3ë*ìsí^î�ïMð°ñÂòBó�ó�ôKõð�ía�3ûÈþÿõù î�ð`ñ©ð>ñ ù#ù û ù þ ù í�î�ð � 8 íBôÅî�ð]�ö°ë(b©ð�ïMþ'òÂûL�3ó�ô�õð�íP�"1�kî�ï�3ó?î��³ñ�õù "Âô ûZ�ac�lïMôL�3ó�ô ð�í��3ûü°ë32%ï¥ð � ï�3þ)�ló�ôKõð�íd� ù �6�1�3ó�ôÅð �]ñ ù�ù û ù þ ù í^î�ð]� 8 íÂô î�ð � ù í�ñ©ð �ecH�lïMô��"Âû ù ��©ë $ ï ù c ù ô í^î�ï¥ð`ñBòBó�ó�ôKõð�íP�³ûL�³ó)ð�í]c ù ï ��ù íBó�ôL�

Page 6: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

fÇÜÞÝ ßàxáOâ<ã´â�äg@�C�ç�à*éh@sà%äiB æ\@�áDCsè´é�ä�âÙ ê�ë%ìkí^î�ï¥ð`ñBòÂó�ó�ô�õð�íÙ ö`ë0��ð�í1��ô��kî ù íBó�ô��Ù ü`ë.+ �fù �kîj�"Gô û ôYñ��3ñ

Page 7: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

:k< â?>A@sà.B é�ä

Page 8: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...
Page 9: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

Û|ÜØÝ ßàxáOâ�ã³âUäåã³à æ´ç è´é�ä�âê3ë ê�ë ê3ë ¬�h)zUrAq.h)�3e1qU��}lodlnmopl7qdr ¢Z�slut ¢�vwr ¡´glh"e?nlz|y~cfo�}Ag3e"b.h?u{}ljky��h)gjkh)g�cfy{g�}3e%osgJtyx�£{z�£v��Ze�r�osb.e?q8nAo���}lo}|~t���v�r�x��yqposbȲ`y~rlb.ji¦lyªcfÃ5osg�jse?n3e�y~g�cfosqm±1e?u{he?jkh?cie1nlhl�OaGµZrlu{y~j�e?qpr�h)qp��}8�o*osbmcfh|glhUjkh)g�cfq.e?nly{jko*osu°cfokh)q.okz�e�nlo*oѵAy~bdc.osgljkyweA�ê3ë ê�ë~ö°ë e�v¬�h)zUrAq.h)�3e1qÂ��}lo�|�tL�]v�r�� � �N��glh]osb�²`y{rAb.ji¦lyªcfÃ�okg�gly{gA�È�}lg�y~g�cfosqm±1e?u{h��}lo*jsh?g�c.osgl�)e�e?u°jkosqdhl��Ivp¹�e1u{uwe1q8cfqdosbÉb.h?u{}ljky{h)glokbÉnlo}lnm7r�� l�������q��l�tY¢4vNr ¢A�3okgd��r�t�x%£4z�£vÑ�� jjvÉ»�qdh)�3e?qp��}lo%osu`rlqdh)�lu~oszUe�e?g�cfosqdy{h)qÉe1nlzUyªcfox}Ag3e��}Agly{jse�bdh)u{}Ajsy��h?g��(q��ê3ë ê�ë~ü°ë a�b.jkq.y~�ly{qpu{e�osjs}le?jsy��h)g�u~y{glose?u

ln�j�oa� �#� � l��*� � �o�������oa� � l m oP����l0r ¢okg�u{e�ÄÅh)q.zUe0�.mHr O �ÿjkh)gd��r�t�l z�l�m�zj T j 6z¡l �#� � � v8� O }Ag3e|zUe1c.q.y{Ã3¢J£�¢G�

ê3ë ê�ë¤�©ë ºZose.l m r O l�jkh)g¥lw¦d§ � � O ¦�¨ ��©*� tL§3vÑ�O»Oqdh)�3e?q:��}lo�u{e�jsh)glbmcie?g�c.onlo:²`y{rAb.ji¦lyªcfÃ�jsh?q.q.okb.r�h)glnly~osg�cfoOokb1ªAr z�e¥µ � «�¬ nlh?glnloOu{h)b «�¬ bdh)g�u~h)b`e?}Zcfh�±1e?u{h)qdosbnlo O/­ � O �At�®Éosjs}8�osq.nAosb.o���}loUcfhKn3e�zUe1cfqdy{Ã�b.y~z\�o�cfqdy{j�eÇnlywe1�)h)g3e?u~y{Ãse�osgÊ}lg3e��3e?b.oh)qmcfh)gAh)q.zUe?u�vÑ�ê3ë~ö`ë ê3ë ��rlu~y{j�e1q]okuGz\�okcfhKnlhUnlo�a�}lu{okqxjsh?gJ¯�r £°M�l�]l*�±rÿ£)�Prle?qfe�e1rlq.h�µZy{zUe?ql�tm£v5nlh)glnlohl#okb�u{e�b.h)u~}ljsy��h)g'nlo?l�m�r²x/lnq���lut ¢�v3rå£)�U¬�h)z|r3e?qfe1q�osuOosqdq.h)q�qdo�e?ujkh)g�oku`rlq.o�±Ky{bdc.h�osgÇosu°cfokh)q.okz�e�jkh)q.qdosb.r�h)glnAy{osg�c.o?�ê3ë~ö`ë~ö°ë a�g|uwe�b.okjsjky��h)gUe?g�cfokq.y{h?qG±Ky{z|h)b���}lo�lnmHrk� l��³����q���l�tY¢�vNr ¢�c.y{okgloÉz�}lji¦3e?bbdh)u{}ljky{h)gAosb3t nlo]¦losji¦lh�y~gAÁ3glyªcie?b�v��7´�e�jk}É�e?u�nlo�oku{uwe1b:jkh)g�±)okq.�)oxoku^zÊ�okc.hZnAh�nlo�aO}Au{osq�µºZ}Ar^h)gAy{osgAnlhU��}lo�e�j�e?}AbfeUnAo�jky{osqmcfh)bpokq.qdh)q.okb]nlo%q.oknlh)glnAosh�okg�qdo�e?u~y{n3e1nÇbdo%e?rlu{y~j�eoku`z\�o�cfhKnlh�nlo%a�}lu{okq5jkh)g¶l{�Dr £�¢ � � � � ´¥e���}8�o%b.h)u~}ljsy��h)g�jsh?g�±?osqd�)o�µê3ë~ö`ë~ü°ë e�v%¹]e?u{u{e?q�}lg3eÇÄ1�h)q.z�}Auwe�r3e?q.e<uwe�l � js}le?glnlh#bdo�e?rAu{y{jseÇoku8zÊ�okc.hZnAh�nloa�}lu~osqÉe·lnm7r¹¸1lVo»ºO�lut ¢�vNr ¢Z�3jsh)g¶l{�Dr ¢A��IvB¬Èe?u{jk}luwe1qBu{eɱ?osqdn3e?nlokqfexb.h?u{}ljky��h)g*�*jsh)z|rlqdh)�3e?qB��}lo.� lut�¼6vx.l{½}�*¾ ¢]jk}3e?glnAh¯w¾ ¢�jsh)g�� ½»r¿¼3À+¢A�Á j�v%a�g>uwe?b%jsh?glnly{jky{h)gAosb%nlosu8e?r3e?qmcie?nAh#e?g�cfokq.y~h)q�nAosz|h)bdc.qfe?q%��}lo�bdy¸=Ãr×¢�b.ojk}lzUrAu{o}� l�t�¼Äv*xÅl{½}�{r¹ÆwtǯIv`r^okq.h¥� lut�¼Äv*xÅl{½}�{rÈÆ¥tǯ4Év©glhxb.o8js}lz|rlu~o�r3e?q.e]gly~gl���}lgÊ À £)�

£

Page 10: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ê3ë~ö`ë¤�©ë ®Éosr�okc.y{qposu`rAq.h)�lu~oszUe�e?g�cfokq.y{h?qpr3e?qfe�oku`b.y{bmcfokz�etLl � v m r ¡*l � o�¡*l qtLl q v m r ¡*l q

jkh)gdl�tY¢4v~r�tm£{z�£vÌË`�ê3ë~ö`ëÍ�°ë »�q.h?�3e?qp��}lo%osu`z\�okcfhKnlh�nlo%a�}lu~osqÉjsh)g¶l{�Dr ¢�e?rAu{y{jse?nlh�e0l�m7r £Do»�Iq��l�tY¢�v�r ¢�glh�okbÈnlo]h)q.nlokgÇ¡Z��ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3tÇ£Tq�o³¡*q]o�×{q�oa������o)Ø7qsrÙtY¡4Ø�o�£v6tm£1o¡�oP×eo� j j ÚØHv¡°{×A�ê3ë~ö`ëÍ�°ë »Oqdh)�3e?q���}lo�osuÉz\�o�cfhKnlh'nlo�aO}Au{osq|jsh?gPl*�Ûr ¢´e?rlu{y~j�e?nAh´okgÝÜ ¢Hz�£TÞ5el�m7r��1tУ�x?�]v��Hl�tY¢4vNr ¢*js}lz|rlu{o�� lutУvHxwl{½}��ß¹¯q8��b.y{g�okz��3e?qd�)h�gAh%okb8nAo5h?q.nlokgnlh?bs�ê3ë~ö`ë � ë �5g�jsh)glnA}ljkc.h)qÉr^h)qp}Ag3e�j�e?qdq.okc.osq.e�jkh)zUe?q.jse?u^±?o%}Ag3e�b.o� g3e1u°��}lo*y{glnly~j�e«¡®ÉosnA}lÃsjse�ewà?¢1¯l��}lg<q.e1cfhUnlosbdrl}8�osb�h?cfq.eU��}lo�y~glnly~j�e³«¡®5oknl}lÃkj�e�e|��¢?¯l��z��e?b�e1nlo��u{e?g�cfo%b.o%osgljk}losg�cfq.eA�P�)e�eUrle?b.hUnlo�c.h)qdc.}l��eA��jsh?g<h?c.qfe?b]e?gÉ�e?u~h)��e?bÉnloÅ×)¢A�^¡?¢��´£�¢A�§Gy~g3e?u~zUokg�c.o?�Z}lg3e��}lu~c.y{zUe�b.o� g3e?u`y{gAnly{jse'«¡á�y{okg�±)osgAy{nlh)b5e·®Éosnl}lÃkj�e?¯A�e�v5avµZrlu~y{jse?q]��}8�o�q.okuwe?jky��h)gÇ�)}3e?qdn3e�okuÂji¦ly~bdc.oâtÇ´µv�e1g�c.osqdy{h)q5jsh)g<osuBz\�o�cfhKnlh�nloa�}lu~osq�e?rlu{y~j�e?nAh�e�tÇà1¢�xã�]v�l�m�r £�tÅy{g�cfokq.rlqdokcie1q(�Êjkh)z|h�u{eÇnly~bdcfe?gljsy{e�o¥l#jkh)zUhoku©c.y{okzUr�h�v8��jk}É�e?g�cfh|cie?qdn3e?q3�e�osu©jkh)glnl}lj�cfh)q5osg�u{u~os��e?qÉeh®Éosnl}lÃkj�e�bdy©¦3e?jso%j�e1b.h�ec.hZn3e1bpuwe?bpbdoK g3e?u~osbs��Iv�ºZy�¦K}A�ly{okqfe>y{gZÁ3gly~cfe?b�bdoK g3e?u~osbs�Éokb.r3e?jkywe?nle?b�y{gAÁlgly~c.osb.y~z�e1u{z|osg�cfo1�e´�u~u{ok��e?qs�� ee?u~�)}lg3e�±?osÃ�e·®5oknl}lÃsjse�µê3ë~ö`ëÍ °ë Æ�e?nlh�osuOrlq.h?�lu{okz�e�l m räl���lut ¢�vVrÚ£)�Bb.o�edl � osu:q.okb.}luªcie?nAh<nlo|uwe�¢���okb.y{zUe�y~c.osq.e?jsy��h)gÇe?u`e?rlu~y{jse?qÈosu`zÊ�okc.hZnAh|nAo�a�}lu~osqpjkh)g�rle?b.h¥¯At o}l*�sr&£v���b.osehå �u~h�zUy~b.z|h�r3e?qfe�r3e1b.h¥¯ °?¡Z�OÆxosz|h)bdc.qfe?q��K}Ao.l �0æ å q �0æ l�tL� � v��� ê3ë~ö°ë�& »�q.h?�3e?q���}lo�oku^zÊ�okc.hZnAh�nlo�a�}lu~osqÈe1rlu{y~j�e?nlh�eÅl mèç £exA�âr�£)�7lut ¢�v~r ¢c.y{osgAo�h)qdnlosg�okbdc.q.y{j�cie?z|osg�c.o�£°)¡*js}3e1glnlh�bdo�e?rlu~y{j�e*osg�Ü ¢Hzs£TÞÏ�Kosb�nlosjky{qs�K��}lo¥� lutУv�xl{½}��r²Æwt�¯]����qÄv%r�osq.h�� lutУvDxél{½}��ÃrêÆwt�¯�É�v%r3e?q.e Ê ÀÚ£°?¡Z��aGµZrlu{y~j�e?q�j`�h)z|h#osbokbdcfhÇr�h)b.y~�lu{o�bdy:¦le?�`�� e1zUh)b�rlq.h)�le?nlhÇ�K}AoUoku:zÊ�okc.hZnAhÇnAo�a�}lu~osq�osb%nlo|h)q.nAosg´}lglhl�ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3tU�Écfy~u{y{Ãse?qOosu�cfosh?q.oszUe�nloku^±1e?u{h?q8z|osnly~h�r3e?q.e�rlqdh)�3e?q ç ¢?o £Zx ç ¢ 棰 ç �4¢ æ ç ¢âx ç ¢âx�£1�

¡

Page 11: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÌÎÍ ê3ë{ö°ë ê�+`ë ¬�h)glbdy{n8�okq.osbdo�oku`rlq.h?�lu{okz�e�jkh)gÛë�r ¡l m ríì x]Õ4î x]�Õ4ï ×dð l z l�tY¢4vNrXì ¢x]Õ4×4ð  

�]rlq.h�µZy{zUe?q0l�tm£v�z|osnAywe?g�cfo�okuÉz\�o�cfhKnlh'nloÇaO}Au{osq�jkh)g�¯�r £°{×)¢Z�Zl*��rXlut ¢�v%�jkh)zUrle?qfe?qGosulqdosb.}Au~cie1nlh*jsh)g|uwexbdh)u{}ljky��h)g�qdo�e?uHlutУv~r�tУTm ��ïK£às j j Äzjxx¡M�{mÎÕ?��ï{ñò j j ¡v Ë ��Bqfe1cfe?q:nlo�oѵArAu{y{jse?q:uwe*�)qfe?gUnly{bdr3e?qdy{n3e?n|osg�osu�q.osbd}lu~cfe?nlhl�òtÏ� �e?b�e?nlokuwe?g�cfo]nly{qdosz|h)b��}lo�okbdcfh?bpb.y{bmcfokz�e�okg�u{h)b8��}lo�osu°zÊ�okc.hZnAh�nlo�a�}lu~osqÈglh?bÈrl}loknlo�n3e?qÈbdh)q.rAq.osb.e?bpb.h?góTô�õ�ö v��ÌÎÍ ê3ë~ö`ë ê�ê3ë �]rlq.h�µZy{zUe?q~l�tÏ¡4v©nlh)glnAoel�osbOuwexbdh)u{}Ajsy��h?g�nloòlnmHr�� l�������q���l�tY¢�v�r ¢A�}Ac.y{u~y{Ã�e1glnlh|osuGzÊ�okc.hZnAh�nlo�a�}lu~osq�jkh)g�l{�3r ¢Uo�l{�3r £�¢ �n÷ ��¯�r^ok��}lo� glh�okg'j�e?n3ejse?b.hl�:aGµZrlu{y~j�e?q�uwe�nly~ÄÅokq.okgljsy{e�okg�u~h)bÈqdosb.}Au~cie1nlh)bs�ê3ë~ü`ë ê3ë ¹�e?u~uwe?qp}Ag3e|Ä1�h)qdz�}lu{e|r3e1qfe?l � js}3e1glnlh�bdo�e?rlu~y{jse�u{eUqdos�)u{e|nlokuBc.qfe?r�osjky{he�osjk}3e?jky{h)glokb]nAo%u{e�ÄÅh)q.zUe�l�m7r¿��lVoP¼]jsh)g¶lut ¢�vNr ¢Z�ê3ë~ü`ë~ö°ë ��rlu~y{jse?q8u{e�qdos�)u{e�nloku^cfq.e?r�osjsy~h�okg\Ü ¢Hzs£TÞ^eÅlnmHr ¡*l^�nl�tY¢�v~r�£xrlq.h?�3e?glnlh��}loíøç l4½ùr újqy� ½ o�Æwt�û �n÷ v��ÞÆxosnl}Ajsy{q�nlo³e?¦°�� ��}lo¹� l�tm£vex�l{½}�±r Æwt�¯�qÚv��ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3t�²©e%nAosb.y~�)}3e?u~n3e?nÇ£�oÛ�Âß¹ú ­ y{z|rlu{y~j�e·tm£üoJÆ¥t�û �n÷ v¡v ½ r�£�o�Æ¥t�û � qÚv��ê3ë~ü`ë~ü°ë ®Éosjs}8�osq.nAosb.oÇ��}lo�uwe#qdos�)u{e#nlosu8cfqfe1r^okjsy{h�okgˬ��e?u{jk}lu{h'­5}lz\�okq.y~jsh�®%osqfe}lgle´ÄÅh)qdz�}luwe�nloÇjs}le?nlqfeMcf}lq.e³g�}lz\�osq.y~j�e´�K}Ao#e?rlqdh�µAy~z�e1�3e\ý�þÿ |~t���v¥ë4�¶t nly~��e?z|h)bjkh)gw|�À+¢*r3e?q.e*ÁM·.e?qOy{nlose?bÚv�r^h?q�osu]�e?q.ose%nAo]u{e*jkh)u{okjsjky��h)g|nloÉcfqfe1r^okjsy{h?b:nAo5±��osqmcfy~jsosbt�����zi¢�vÑ�7tL����zÚ|~tL����v¡v��7t������ � zi¢�vÑ�Ht������ � zÐ|�tL���Lv�v��ÂaGµArAu{y{jse?q°r�h)q`��}8�oOq.okjsy{��o�osbmcfoOglh)z��lq.ocfe?z��ly��osg�osu`zÊ�okc.hZnAh|y~zUrAuÒ�� jky~c.h�nlo*okbdcie|b.okjsjsy��h)g°�ê3ë~ü`ë¤�©ë ºZy{�?}ly{okglnlh�uwe�y{nloseÇnAosuOoзdokq.jsy~jsy~h<e?g�c.osq.y~h)qs�©oѵArAu{y{jse?q*r^h?q���}8�o|uwe�q.ok�)uwenlo|ºKy{z|rlb.h)g�gAhÇnle�u{}l��e1q�e�}lg'z\�o�cfhKnlh�}lgly~r3e?bdhl�`osb�nlokjsy~qs�`osg'okuv��}lo·l � � � bl�h)u{hnlokr^okgln3e�nlo}l � �lnlo}� � ��nloů°�� ê3ë~ü°ë�� ÆxokzUh)bmcfq.e?q���}lo<jk}3e?glnlh´uwe�qdos�)u{e´nlokuÈcfq.e?r^okjsy~h³bdo<e?rAu{y{jse'e´rlqdh)�lu~o��zUe?b�osbdj�e?u{e?q.okb�nAosuxcfy~r^h l�m�r |~tL�]v�okg�Ü ¢Hz�£TÞ*bdo'js}lz|rlu{o���}lo�� l�tL� � v±xÝl � � æ¢ m ¡4à�¯ q b.}lr·� | m m � �ÌÎÍ ê�ë~ü°ëÍ�°ë �]rlu{y~j�e?q5uwe|q.os�?uweUnAosuÂc.qfe?r�osjky{hUjsh)g\¯�r�¢*m ¡|r3e?qfe�e?rlq.h�µZy{zUe?qelutУvnlh?glnlo3l�okbdc3�e�nlokc.osqdzUy~g3e?n3e*r^h?qDl�m7r��/o�lnq��©�7l�tY¢�v�r £)�O¬�h)z|r3e?q.e?qOosu�q.okb.}luªcie?nlhjkh)g�u{e�b.h)u~}ljsy��h)g�q.ose?uÏ�

×

Page 12: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÌÎÍ ê3ë~ü`ë � ë ¬�h?z��ly{gle?qÈosuPz\�o�cfhKnlh�nlo*­]o��pcfh)gÇr3e?q.e�q.okb.h)uª±)osqpokjs}3e1jsy{h?glosb.t okbdc.hokbs�/� � � � r � � xÝ|~tL� � v¡°4|ImLtL� � v¡v|jsh)gÔuwe³q.os�?uwe>nloku�cfq.e?r^okjsy~h>osgÔ}lgÔrlqdh)�)qfe1z�e§BÓV®G��®É�x­���}lo�n3e1nlhU}AgÛl{�3¦ãtyx�£{z�£vpe?rlqdh�µZy~zUo1�3nlo�okbdcfeUzUe?glosq.eA�3uwe�b.h?u{}ljky��h)gnlo}l�m7r jsh?b�l^�7lut ¢�vNr¹l*���ê3ë¤�Bë ê3ë ¬�h)z|rlqdh)�3e?qÉ��}lo%osu`z\�okcfhKnlh�nlo*�Âe��Ku~h)qÉnlo*h)q.nlokgÛ×|e?rlu~y{jse?nlh�e?u`rlqdh)�Z�u~oszUe�l m r ¡#�Il^�Hlut ¢�vNr�£)�3u~u{o�±?e�e�u{e�y~cfokqfe?jky��h)g

l � � � r�l � oP¯��m¡� � l � oal � tУDo�¡#� q� v¡¯.o�¡#� � l � t�×eo�¡� q� v ¯�q×�  ê3ë¤�Bë~ö°ë ¬�h)gAbdcfqd}ly{qÉoku°z\�o�cfhKnlh�nlo*�Ge��Ku{h?qp�)osglokqfe?u`nAo%h?q.nlokgÛ×�r3e?q.ehëÅr £)�ê3ë¤�Bë~ü°ë ¬�h)gAbdcfqd}ly{qÉoku°z\�o�cfhKnlh�nlo*�Ge��Ku{h?qp�)osglokqfe?u`nAo%h?q.nlokg#¡�r3e?q.ehëÅr ¡Z�ê3ë¤�Bë¤�©ë e�v°a�b.jsqdy{�ly~q°uwe�Ä1�h?q.z�}lu{e�y~c.osq.e1cfyª±?e8jsh)qdq.osbdr^h?glnly{okg�cfo:e?u)z\�okc.hZnlhpnAo:�Âe��Ku{h)qnlo�h)q.nAosg�ØËrle?qfe"u{e³okjs}3e?jky��h)gÝtű)okjkc.h)q.y{e?u�v�l m r O l\jsh)g O }lg3e"zUe1c.q.y{Ã�jkh)glbm�cfe?g�cfo}¢J£�¢G�Á �IvȬ�h?zUrlqdh)�3e?q:��}loxÄÅh)qdz�e?u~zUokg�cfoÉjs}3e1glnlhhØ·r� �3e?bmcie�c.h)zUe?qÂûêr £0t }lg3eyªcfosq.e?jsy��h)gIv8rle?qfe�h)�Ac.osglokqÉuwe�b.h)u~}ljsy��h)g�o�µAe?j�cieA�ê3ë¤�BëÍ�°ë Æ�e?nle�u{e�ÄÅ}lgljky��h)g Ê t4§Ýx]¾ tyx�£4zs£v

Ê t��]v�r ¡ç �� ��� ú*� ­�� ë4�Ðzbdo�nlokÁ3gAo0l¶r�lut��]v]jsh?zUh�u{eUÄÅ}lgljky��h)g�y~g�±)osqdbfe�nlo Ê t cie?uBÄÅ}lgljky��h)g�okbxz�}A� �}Acfy~uÂokga�bdcfe?n`�� bdcfy~j�e�vÑ�e�vxÆxokzUh)bmcfq.e?qx��}lo�cie?uGÄÅ}Agljsy��h)g'y{g�±)okq.bfe�o�µZy~bdcfo���b.e1cfy~bdÄ e?jko�uwe�okjs}3e?jky��h)g´nlyªÄÅo��qdosgljkywe?u l m r ç �¡ ú�� � z l�tY¢�v~r ¢H 

�IvBaObdjsqdy{�ly~qÂu{e5yªcfosq.e?jsy��h)g%jsh)qdq.osbdr^h?glnly{okg�cfope?uKz\�okcfhKnlh5nlo��Âe��Ku{h)qÂnlo�h)qdnlosg�cfq.okbs�ÌÎÍ ê�ë¤�©ëÍ�°ë a�bdjsq.y~�ly{qÂ}lg�rlqdh)�)qfe1z�e]§ÂÓV®G��®É�x­Ë�K}Aopn3e?nlhx}Ag·¸»¦ t�x � °)¡7z � °)¡4ve?rAq.h�µZy{z|o�uwe�b.h?u{}ljky��h)g�nlo*u{e�okjs}3e1jsy��h?gÇnAosu©r8�osgAnl}lu{hl m m o\b.okg/l�r ¢Hz l m t ¢�vNr ¢Hz lut ¢�vNrȸZz

Page 13: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

okzUrlu~o�e?gAnlh*osu�z\�o�cfhKnlh*nlo]aO}Au{osq���oku3nlo]�Âe��Ku{h)qOnlo5h)q.nAosg�nAh)b/t r3e?q.e%oku{u~h%¦le�����}lojkh)zUokglÃ�e1q5okb.jkq.y{�Ay{osgAnlhUu{e�osjs}le?jsy��h)g<jkh)zUh�}lgleUnlo*rlqdy{z|osqÉh)q.nAosgIvÑ�Èa�g#�Çosj`�e1gly{jseokb]jkh)glhKjsy{nAh|��}lo%osu©rlqdy{z|osqȱ1e?u~h)qpr^h?b.y~c.y~±?h|nAo}�#jsh)g¶lnm�tL�]vZr ¢dt osu ó����hõ������¡õ�� �!� v±Ky{okglo*n3e?nlh�jkh)g��?qfe?gÇe?rlqdh�µAy~z�e1jsy��h?g�r^h)qpu{e�Ä1�h)q.z�}luwe� tm£Do £� bdosg q ¸ ¡ o ñ

Õ?� bdosg#" ¸ ¡ vР�Écfy{u~y{Ãse?q�osbmcfo�q.okb.}luªcie?nAh�r3e?q.e�jsh)z|rlqdh)�3e?q:uwe%rlq.okjsy{bdy��h)g�nlo�e?z���h)b8z\�o�cfhKnlh)b�bdos���}lg±1e?qs�� e�uwe�u~h)gl�)yªcf}ln�nAosu`r3e?bdhl�

ê3ëÍ�`ë ê3ë ¹]e?u{u{e?q�u{e?bpjsh)gAbdcie1g�c.osb/¸>�âº"nlo�ÄÅh)qdz�e���}lol � � � r¹l � oP¸~¯I|~t�� � � � z¡l � � � vüoaº1¯I|~tL� � z�l � vbdo�e�jsh)glbdy{bmcfosg�c.o�nlo*h)qdnlosgÇ}lglh|h�jsh)gAb.y{bmcfokg�c.o�nAo%h?q.nlokg�nlh?bs�

ê3ëÍ�`ë~ö°ë e�vȹ]e?u{u{e?qÈoku`h)q.nlokg�nlo�jkh)glbdy{bdc.osgljkywe�nloku`z\�o�cfhKnlhl � � � rÈl � x à ¡ ¯I|~tL� � z�l � vüo ï ¡ ¯I|~tL� � o ¯ ï z�l � o ¯ ï |~tL� � z�l � v�vÄ 

�Iv©¬�h)z|rlq.h?�3e?qZt bd}lr�h)gly{okglnlhl�¥jkh)zUhÉbdy{z|rlq.o1�M��}loD|�osbB²`y{rlbdji¦ly~c.Ã�osg%uwepb.ok�)}lglnle±1e?qdywe?�lu~o�v°��}lo�okuAz\�okc.hZnlh5bfeMcfy{bmÄ e?jso8uwe?bBjsh?glnly{jky{h)gAosbGnAosu�cfosh?q.oszUe]nAo�jsh?g�±?osqd�)osgljkyweA�ê3ëÍ�`ë~ü°ë a�u`z\�okcfhKnlh�nlo%a�}lu{okqpzUhKnlyªÁ3j�e?nAh�osbÉ}lgÇz\�o�cfhKnlh�nlo*}lg�rle?b.h�jsh?g$ tL��z�l z�%A¸Ð¯IvNrÈ|~tL�0o ¯ ¡ z�lVo ¯ ¡ |~tL��z�lHv¡vРe�vÈÆxokzUh)bmcfq.e?qp��}lo�cfy{okglo*h)q.nAosgÇnlo*jsh)g�±)okq.�)okgljsy{eUnlh?bs��IvxÆxokzUh)bmcfq.e?qs�^�l}lb.jse?glnlhÇe?u~�È�}lg#jkh)g�cfqfe1oзdosz|rlu~hl�P��}lo�osuGh)q.nlokg�glh�osb�zUe��)h)q��}lo*nlh)bk�ê3ëÍ�`ë¤�©ë a�uvrlqdh)rÉ�h)bdy~c.h�nlo�osbmcfo�rlq.h?�lu{okz�e�okb*zUh)bmcfq.e?qx��}lo�u{h)b�z\�o�cfhKnlh)bxnlo�}Agr3e1b.h<gAh�bdh)g"u~h)b\�}Agly{jkh)b*r^h)bdy{�lu~osbk��¹5y{bdc3�h)q.y~j�e?z|osg�c.o|}Aglh<nlo|u{h?b%rAq.y{z|osqdh)bxÄÅ}lo|osu& Õ'�(ÌÖ Ñ Ö Ñ '*) ÒÇÓ¡Ô,+�Ñ?�Mosg�okuK��}lo:glh]b.o:nly{bdjsq.o�cfy~Ã�e]bdy{glh5��}lo�bdo8jkh)glbdy{nlokqfe]}Ag3e]bd}ljsokb.y��h?gnloxÄÅ}Agljsy~h)glosbk�.-l � tL�]v�/10�32 � �A�K}Ao*c.qfe1cfe?g�nlo*e?rAq.h�µZy{zUe?qÈe�uwe�±?osqdn3e?nlokqfe�b.h)u~}ljsy��h)g��okbdc��e1g�nlo�Á3gly~n3e?bÉr^h?q

l � � � t��]v�rÈlut��nvuo �ÿ |~t��Ðz�l � t���v¡vNë4�à

Page 14: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

e�vÉ��rlu~y{j�e1q5okuGz\�okc.hZnlhUnlo�»�y~j�e?qdn�e¥l m r�l��]l�tY¢4vÂr £�jsh)g�l � uwe�ÄÅ}lgljky��h)g#��}lo±1e?u~o�jsh)glbmcie?g�c.osz|osg�cfo%}lglhl�� �Ivx�]rlu{y~j�e?qxoku�cfosh?q.oszUe�nlo|uwe�e?rlu~y{jse?jsy��h)g�jsh)g�c.qfe?j�cfy~±1e\t hÇnloku:rA}lg�cfh�Á1·dh�v�e?uz\�okc.hZnlh�nlo�»�y{j�e1q.n�r3e?q.e�rlq.h?�3e?q�}lg#c.osh)qdoszUe�nlo�o�µZy{bmcfokgljsy{e��<}lgly~jsy{nle?n#r3e?q.e�osurlqdh)�lu~oszUe�lnm7rp|�tL��z�lHv��7lut��7vNr54^�ÌÎÍ ê3ëÍ�`ëÍ�°ë a�uwe?��h)qfe1q%}Ag>rlq.h?�)qfe?zUe�§BÓ}®Â��®5��­ ��}lo�e1rlu{y~�K}Ao|oku8zÊ�okc.hZnAh�nloa�}lu~osqvz|hZnAy~Á3jse?nlh�exu{exosjs}le?jsy��h)g0l m r xe� q l��4l�tY¢�vNr&£)�)����}loÉz�}lokbdc.q.oposuZcie?zUe� glhqdo�e?u�nloku�okq.qdh)q:e?u�e?rlq.h�µZy{zUe?qNl�tÏ¡4vvokg�q.okuwe?jky��h)g�jkh)g�u{e%jkh?cie*r3e?q.e%oku^okq.q.h?q:h?�Acfokgly{n3ejkh)g�oku°cfokh)q.okz�e�jsh?q.q.okb.r�h)glnly~osg�cfo1�ÌÎÍ ê3ëÍ�`ëÍ�°ë a�u~os�)y~qx}lg'z\�o�cfhKnlh�nlo�h)qdnlosg'nlh?b*�<osbdjsq.y~�ly{q�}lg'rlq.h)�?qfe?zUe�§BÓ}®È���®É�x­���}lo*u{h|e?rlu~y{��}loxrle?qfe�osbmcfy{zUe?qsl�t�×4v8osgÇj�e?nle|}lgAhUnlo*u~h)bprlq.h?�lu{okz�e?b

l m r76 l7q b.yül¥ß ¡£ b.yül¥À�¡ l m r76 lnq b.y�l¥ß ¡

� b.y�l¥À�¡ l m r86 lnq bdyülwß ¡x5�3o\�4l bdyülwÀ�¡jkh)gdl*�sr¹lut ¢�vNr�£*osg�c.hZnAh)bpu{h)bÉjse?b.h)bk�Ȭ�h?zUr3e1qfe?qpu~h)bpq.okb.}lu{e?nlh)bÉh)�Ac.osgly~nlh)bÉjsh?gu{e?b�b.h)u~}ljsy~h)glokb�o�µAe?jkcfe?b:�{m¤àZ�3£�¡x�0ú*� � o'£)��b.ok�È�}lg�b.o5zUhKnly~Álj�e�oku3r3e?b.hA��c.qfe1cfe?glnlh*nlonloknl}ljky{q:osz|r`�� qdy{j�e1zUokg�c.oÉosg�jse?n3e�jse?b.h�js}É�e?u�r3e1q.osjko�bdosq�oku^h?q.nlokg�nlo5jsh)g�±)okq.�)okgljsy{enloku©e?u{�?h)q.yªcfz|hl�

ê3ëÍ�`ë ê3ë aGµZrlu{y~j�e?q�r�h)q���}8�o�oku�z\�o�cfhKnlh>nlo´a�}lu{okq�z|hZnlyªÁ3j�e1nlh>osb�okg �?osglokqfe?uz|oзdh)q��K}Ao�uwe>q.ok�)uwe³nlosuxc.qfe?r�osjky{hl�Ù´�aOb�u{e>q.ok�)uwe"nAosuxcfq.e?r�osjsy~h>}lgÔz\�okcfhKnlhÊnlo®É}lgl�)oÑ�:9�}Acdcie�µê3ëÍ�`ë~ö°ë a�b.jkq.y~�ly{qOosu3cfe?�lu{okq.h*��}lo�jkh)q.qdosbdr^h)gAnlo�e1u�bdy{�)}Ay{osg�c.o5zÊ�okc.hZnAh%jkq.ose?nlh�r�h)q¹5os}lg

l � � � rÈl � o ¯ �<; |~t�� � z¡l � v�o»×�| � � � o ¡{¯× z¡l � o ¡{¯× |�tL� � o ¯ × z�l � o ¯ × |~tL� � z�l � v�v ��=ê3ëÍ�`ë~ü°ë �]rlu{y~j�e?q]osuvzÊ�okc.hZnAh�nlosuGrlq.h)�Au{oszUe�e?g�c.osq.y~h)qxewl m rÙl^�]lut ¢�v�rÙl{�VrÞ£¦3e1u{uwe1glnlhVl � ��jsh)z|rlqdh)�3e?q�nly~q.okjkcie1zUokg�c.oÉ�K}Ao5rle?qfe*osbmcfo5rlq.h)�Au{oszUexosbOnlo5h)qdnlosg?×A�ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3tUa�z|rlu{ose?q:�K}Ao�£~o)¯3oA¯qÄ°)¡�oA¯ ÷ °?Õ(r¿ú?>~o�Æ¥tǯ " vO�U��}lohtm£1o\�]v � r£DoPÆ¥t�¢ �]v�js}3e?gAnlh?¢Z� �N�nß�£)�

Õ

Page 15: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ê3ëÍ�`ë¤�©ë a�g u{h)b�z\�okcfhKnlh)b�nlo�®É}lgl�)oÑ�:9�}Ac.cfeËy~zUrluÏ�� jky~cfh?b�b.o´nlok�^o³q.osbdh)u~±?osqÇosubdy{bdc.oszUeA�lokg��)okglosq.e?u`glh�u{y~glo�e1uÏ�Ø,�urÈ|~tL� � o�@���¯uz�l � o㯠AB ¬ 2 � �C� ¬ Ø ¬ vÄz D1r £4zi¡7zj j j Äz�E

jkh)g\|>tI§�£�§GF.x]¾ §HF¥�*aOg�okbdc.o�rlq.h)�Au{oszUeUrAq.h)�3e1q.osz|h)b]�K}Ao�n3e?nlh)b/� � ��l � �^osubdy{bdc.oszUe�cfy{okglo�b.h?u{}ljky��h)g �}lgly~j�e�js}le?glnlh¥¯Çokb]bd}AÁ3jsy~osg�cfokzUokg�cfo%r^ok�K}AoK glhl�e�vpºZoseJI�t*§ A F x]¾ § A F n3e?nlh?b5r�h)qKIÝrÙtLI��Ðzj j j 6z�I A v�jkh)gI � t�Ø � zj j j 6zÐØ A vZrÈ|~tL� � o�@���¯uz�l � o㯠AB ¬ 2 � �C� ¬ Ø ¬ vÄ »�q.h?�3e?qv��}loKI bfe1c.y{bdÄ e1jsopuwe]jsh)glnAy{jsy��h)g�nloɲ`y~rlb.ji¦lyªcfÃpjkh)g�jsh)gAbdcie1g�c.oME�qÚ¯Iª|z�e¥µ�� �C� ¬ �tÅnlh)glnlo(ª�okbÉuwe�jsh)gAbdcie1g�c.o%²©y~rlb.ji¦Ay~cfÃ*nlo.|uvÑ��Iv°Æxoknl}ljsy~q`nlosu�e1r3e?qdcfe?nlhÉe?g�c.osq.y~h)qP��nAosu?c.osh)qdoszUeÉnAo:u{eÈe?rlu~y{jse?jsy��h)gxjsh?g�c.qfe?j�cfyª±?e��}lo*osu`bdy{bmcfoszUe�nlosu`okg�}lgljsy{e?nlh�cfy~osglo*b.h?u{}ljky��h)g �}lgly~j�e�jk}3e?glnlh¥¯�okb5r�os��}lo� glhl�

ê3ëÍ�`ëÍ�°ë ��u{h)bÉz\�okcfhKnlh)b5y{z|rluÏ�� jsyªcfh)b8jsh)gÛ�C� ¬ r&¢�b.yONwÀ5D8bdo�u~osb5u{u{e?z�eJP '�& Ò 'RQCSTVU ÕW ÓÄÒ (ÌÖ P��OaGµArAu{y{jse?qÈ��}8�o*±)okg�cfe¥·.e|c.y{okglo�jsh)gÇq.okb.r�osj�cfh�e�u~h)bpy{z|rluÏ�� jsyªcfh)b:�)osgAosqfe1u{osbk�ÌÎÍ ê3ë��°ëÍ�°ë ²©e�b.h)u~}ljsy��h)g�nlo

ì l��lnq�ð m r ì £�¢ £�×x3î x%£�¢4ð ì l��lnqÚð z lut ¢�vNr ì ×ï*ðokbÈr^okq.y��h)nly{jse�nlo]r^okq.y~hZnlh � �Zokg�r3e?qmcfy{jk}luwe1qYXÐl�t � v x�lut ¢�vZXÂr ¢A�[XÐl�t � � v x�lut ¢�vZXsr¢A��¬�h)zUrAq.h)�3e1q%okg>js}p�e?g�cfh<nAy~Á3okq.osg"osbdcfe?b�okjs}3e1jsy{h?glosb%nlo�bdosq�jsy{okqdcfe?b*js}3e?gAnlh#b.ookzUrlu~o�exoku3z\�o�cfhKnlh*nlo5aO}Au{osqv��js}3e?gAnlh�bdoÉosz|rlu{ose*oku3z\�o�cfhKnlh�nlo5a�}lu{okqOzUoE·dh)qfe?nAhl�okg<e?z��^h)bpjse?b.h?b5jkh)gÛ¯wr � °K£�¢)¢A�

ê3ë � ë ê3ë a�b.jkq.y{�Ay{q�uwe1b%jkh)glnly~jsy~h)glosb�nAoUh)qdnlosg�£)�¡��J×Çokg´cZ�osqdzUy~glh)b�nlo]\¼¥� \ê rtУ4z�£4zj T j 6zs£v Ë ��uwe?bvzUe1c.q.y{jkosb O �_^�r nly{e?� t \¼ÄvstÅuwe�zUe1c.q.y{Ã8nlywe1�)h)g3e?uKjsh?g·¼��`�urȼ��Lv��bdy{g�¦3e?jkosqÉq.o�ÄÅosq.okgljsy{eUe�bd}lb]jkh)z|r^h)gAosg�cfokbs�ê3ë � ë~ö°ë e�vÈa�bdjsq.y~�ly{qpoku°cie?�Au{osqdh�nlosu`z\�okc.hZnlh

Ø � r¿|~t�� � o ¯ ¡ z�l � vÐz Ø q r¿|~tL� � o ¯ ¡ z�l � oJ¯IØ � vÄz l � � � rÈl � o ¯ ¡ tÇØ � oJØ q vï

Page 16: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

��jsh)z|rlq.h?�3e?q���}lo�gAh�bfe1c.y{bdÄ e1jso�uwe�jsh)glnAy{jsy��h)g�nlo�bd}lzUe�r^h)q8Á3uwe?b8��okbpnlo�h)q.nAosg�¡Z��Ivp¹�e1u{uwe1q8cfhKnlh)bpu~h)bpz\�okcfhKnlh)bpnAo*cfe?�lu~osq.h@ � ¢ ¢@ q tY¡*º1v � � ¢¼ � ¼ qjkh)g�ºpÃr&¢A�^�K}Ao�glh�b.e1cfy~bdÄ e?��e1g<uwe|jsh)gAnly{jky��h)g�nlo�b.}Az�e|r^h)q5Á3uwe1b5�Çcfokgl��e?g#h?q.nlokgnlh?bs�j�v�aGµZrlu{y~j�e?q�r^h)q���}8�o�gly~gl�)}lgAhÇnAo|u~h)bxz\�okc.hZnlh?b�nlosuOe?rle?qdcfe?nlh�e?g�cfokq.y~h)qxcfy~osglogly~gl�)}lgle�±?osg�cie�·.e|qdosb.r�osj�cfh�e?u°jsh?q.q.okb.r�h)glnly~osg�cfo*jkh)g�@ � r ¢��a@ q r�tY¡*º1v � �8��}lo*b���b.e1cfy~bdÄ e?jko�uwe�jsh)gAnly{jky��h)g�nlo*bd}lz�e�r�h)qÈÁ3uwe1bs�ê3ë � ë~ü°ë e�vɬ�h)z|rlq.h?�3e?qÉ��}lo�u{e�jkh)glnly~jsy��h)g�nlo�bd}lzUeUr�h)qpÁ3uwe?bÉok�K}Ay~±1e?u{o*e|nlosjky{q��}lo*osu`r�h)u~y{glh)z|y{h%nlo*�Âe��Ku~h)qpnlo*h)q.nAosgÇ}lglh|nlo(Ø,�stÅjsh)z|h�ÄÅ}lgljky��h)g�nlo.¯Ç���3e¥·dh|uwe¦ly~rÉ�h?c.osb.y~bpnlo*u{hKj�e?u~y{Ãse?jsy��h)gIv�osb�l m tL� � vüo�@�� l m m t�� � v�¯°��Iv%avµZrlu~y{jse?q*uwe�b.y{�?}ly{okg�c.o|ÄÅq.e?b.o|cfh)zUe?n3e�nlo�Ü ¹]­5¿éÞ8r°�l£�×�¡Kt'«jÜ ²BeÇjsh)gAnly{jky��h)gnlo�b.}lzUe�r^h?q�Á3uwe1b�ÞGÄÅ}Ao�b.}lrA}losbmcie�r^h)qG9�}Ac.cfe�b.y{g�gAy{gl���}lg<jsh)z|osg�cie1q.y{hU�<oѵArAq.osb.e��}lo�cfhKnlh)bpu~h)bÈrl}Ag�c.h)bÉnlh)glnAoÅ|#bdo%o�±1e?u1�}3e�bdh)g�e?rlq.h�µZy{zUe?jky{h)glokbÈnlo�rlqdy{z|osqÈh?q.nlokge�uwe�bdh)u{}Ajsy��h?gl¯l�b Ö1( Ô?t�a�g³u{h)b*oзdokq.jky{jsy~h)b%r^h)bmcfokq.y{h?q.osb%b.}Ar^h)gAnlq.okzUh)b%b.y~osz|rlq.o|��}lo|b.oU±?osqdy~Á3jseu{e�jsh)glnAy{jsy��h)g�nlo*b.}lzUe�r^h?qÈÁ3uwe?bk�lb.y~g<e1nA±)okqdcfy~q.u~h�j�e?n3e�±)okÃ?�ê3ë � ë¤�©ë ¬�h)gAbdcfqd}ly{qpc.hZnlh?bpu{h)bpz\�okc.hZnlh?bpnlo*h)q.nlokg#¡�nlo*u{e�ÄÅh?q.zUe

¢@ q @ q@ ÷ ¢ @ ÷¢ ¢ £a�bdc.}lnly{e?qpb.y©e?u~�)}lglh�c.y{osgAo�h)q.nlokgÛ×Z�

ê3ë � ëÍ�°ë a�gljkh)g�cfqfe1q�cfhKnlh)b�u~h)b�cfe?�lu{okq.h)b�r^h)bdy{�lu~osb�nlo�u{h)b�z\�o�cfhKnlh)b�nAo�®5}lgA�)o��9�}Acdcie�o�µZrluÏ�� jsyªcfh)b�nlo|nlh)b%okcfe?r3e?b%jsh?g³h)qdnlosgË£|�'jkh)g"h?q.nlokgÊ¡Z�U¹�e?u~uwe?qxcfe?z��ly��osgc.hZnlh?bpu{h)bpy~zUrluÏ�� jky~cfh?b8nlo*}lgle|o�cie?r3e�jkh)g�h?q.nlokg#¡Z�ê3ë � ëÍ�°ë Æxo�cfosqdzUy~g3e?qÈoku`h)q.nAosgÇnlosu`z\�okc.hZnlhA�

£¥¤M� £¥¤{î £¥¤{î×�¤M� ×�¤{î ×�¤{¤)¡ £¥¤)¡î

Page 17: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ê3ë � ë � ë ¬�h)zUrAq.h)�3e1q��K}AoËoku�b.y{�?}ly{okg�c.oÊz\�o�cfhKnlhÔy{z|rluÏ�� jsyªcfh�osb´nlo\h)q.nlokg t e?uz|osglh?bÚvs× t�×eo ç ×�v¡°?Õ t�×eo ç ×�v¡°1Õ ¢t�×Vx ç ×{v¡°?Õ x ç ×4°{× t�×eo ç ×�v�°?Õ£¥¤)¡ £¥¤?¡ê3ë � ëÍ °ë Æxoknl}ljky{q�u{e?b�jkh)glnly~jsy{h?glosb�nlo�h)qdnlosg>c.q.osb�bdy{g>z|y{q.e?q�e<uwe�cfosh?q��� e�r3e?qferlqdh)�lu~oszUe?bÈosbdj�e?u{e?q.okb]nAo%u{e�ÄÅh)q.zUe�l�m7rp|~t�lHv��ê3ë � ëÍ&°ë ¹�e?u~uwe?q�cfhKnlh)b�u{h)b8z\�o�cfhKnlh)b�nAoxh)q.nAosg�¡�jsh?g�nlh)bÈo�cie?r3e1b���jkh)ga@ q rc@ � �¼ � r¿¼ q �Z´��py~osglo%e?u~�)}lglh�h)qdnlosgd×�µê3ë � ë ê�+`ë a�gljsh?g�c.qfe?qB}lg3e5b.h)u~}ljsy��h)g%r3e?qfeÉuwe1bBjkh)glnly~jsy~h)glosbBnlo:h)q.nAosg0×Énlo:z�e?gAosqfe��}loUn��o�u~}l��e?q�e�}lg"z\�o�cfhKnlh�oѵZrluÒ�� jsy~c.h�nAow×�o�cie?rle?bât �³h?q.nlokg ×�v�jsh)gd@ q re@ ÷ �¼ q r¿¼ ÷ �OaOu`zÊ�okc.hZnAh|qdosbd}lu~cfe?g�cfo*b.o*jsh?glhZjko*jsh)z|h�z\�o�cfhKnlh�nlo%­5�Kbdc.q3fh)zÇ�ê3ë � ë ê�ê3ë »�q.h)�le?qÉ�K}Ao%u{eg+ 'ih,U Ô¥Ò &GTVU ÕW ÓÄÒ ( ÔwÑ '�UjTVk Ï (ÌÖ&l' Ñ{Ò Ö

l � � � r¹l � oã¯I|m�Ç� � o ¯ ¡ z l � o»l � � �¡ �okb�}lg'z\�o�cfhKnlh�nlo·®É}lgl�)oÑ�:9�}Acdcie�nlo�}Ag3e�okcie1r3eA�%a�b.jsqdy{�ly~qxb.}�cfe?�lu{okq.h��<j�e?u~js}lu{e?qbd}�h)qdnlosgP�

ÌÎÍ ê3ë � ë êKö°ë a�uwe1�^h)q.e?qÈ}lg�rlqdh)�)q.e?z�e�§BÓV®G��®É�x­ ��}lo%e?rlqdh�µAy~zUo3lutУv8osz|rlu~o��e?gAnlh�u{e*qdos�)u{e%y~zUrAuÒ�� jky~cfe�nlosu�rl}Ag�c.h�z|osnly~h�e1u�rAq.h)�lu~oszUeVl m r�x5��¢{l���lut ¢�v~r £5jsh?g¯wr ¢ m £?���Âq.e1cie?qÉnlo*oѵArAu{y{jse?qpr�h)qp��}��o*osu`q.okb.}luªcie?nAh|gAhUokb5�A}losglhA�ê3ëÍ `ë ê3ë »�q.h?�3e?qp��}lo%osu`z\�okcfhKnlh�nlo�cie1�lu{okq.h

¢£¥¤)¡ £¥¤)¡×�¤1� ¢ ×)¤1�¡)¤{ñ £�¤{× ��¤{ñokb5nAo%h?q.nlokgÛ×�r�osq.h|glh��l�

ê3ëÍ `ë~ö°ë ¬�h)gAb.y{nAosqfe1zUh)bpoku`z\�o�cfhKnlh�nlo(®5}Agl�)o��n9�}Ac.cfe�oѵZrluÒ�� jsy~c.h�nlo�cie?�Au{osqdhñ

Page 18: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

¢£�¤1� £¥¤M�£�¤)¡ ¢ £¥¤)¡£ £ x�¡ ¡£¥¤1Õ ¢ ��¤?Õ £¥¤?ÕÓx�Ac.osglokq5oku`h)q.nAosgÇnlosu`z\�okc.hZnlhA�

ê3ëÍ `ë~ü°ë aObdjsh)�?osqUc.q.okb��e?qd�^h)u~osb�nloÇh)q.nAosgéà��\jsh)z|rlqdh)�3e?q|b.yÉb.o�js}lz|rlu~osg�uwe?bjkh)glnly~jsy{h?glosbpnlo*h)qdnlosgÇjsh?q.q.okb.r�h)glnly~osg�cfokb]rle?qfe�osu`z\�okc.hZnlh�nle?nlh|r^h)qpoku°cie?�Au{osqdh¢£¥¤{× £¥¤{×£¥¤{× £¥¤?Õ £¥¤?Õ£¥¤)¡ £¥¤{î ¢ ×�¤{î£ £¥¤)¡ ¢ x/×�°)¡ ¡£¥¤Z£�¢ ¢ ×)¤Z£�¢ ¡)¤4à £�¤4à

ê3ëÍ `ë¤�©ë ¹]e?u{u{e?q�oku��}Agly{jkh�z\�o�cfhKnlh�nlo*h)q.nlokg���jkh)gÇcfe?�lu~osq.h¢@ q @ q@ q ¢ @ q@ " ¢ ¢ @ "¼ � ¼ q ¼ q ¼ �

jkh)zUrAq.h)�3e1glnlh\��}lo'q.o�e1u{z|osg�cfo#c.y{osgAo�osu�h)qdnlosg e?b.ok�)}lq.e?nlhl�8b Ö1( Ô?t�a�u�z\�okcfhKnlhh)�ZcfosgAy{nlh�b.o*u~uwe?zUe�z\�okcfhKnlh�nlo(®É}lgl�)oÑ�:9�}Acdcie�r^h?qÉe?g�cfh)glh?z�e?bdyweA�ê3ëÍ `ëÍ�°ë »�q.h?�3e?qp��}lo%uwe�u{u{e?zUe?n3el+ 'ih,U ÔÅ×�°*îA�ljs}Z�)hUcfe?�lu~osq.h�okb

¢£¥¤*× £¥¤*ס)¤*× x%£°{× ££ £ x%£ ££¥¤*î ×)¤{î ×�¤*î £¥¤{îokb5nAo%h?q.nlokg��l�

ê3ëÍ `ëÍ�°ë »�q.h?�3e?qp��}lo%osu`z\�okcfhKnlh�nlo%¹�e1zUz|osqÐ�й]h?u{u{y~gl�)bo��h)qmcf¦£�¢

Page 19: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

t�×Vx ç ×�v�°?Õ £¥¤1� t�×}x�¡ ç ×4v�°Z£¥¡t�×�o ç ×4v¡°?Õ t�×eo�¡ ç ×�v¡°Z£�¡ £�¤1�£¥¤)¡ £�¤)¡b.e1cfy~bdÄ e?jko:u{e?b©jsh)gAnly{jky{h)glokb©nlo8h?q.nlokg��l�GºZo:rl}losnAo�rlqdh)�3e?q©��}lo:osg�jk}3e?g�cfh�e5h?q.nlokg�osbokuAz|oзdh)qBz\�o�cfhKnlhxnlos®5}lgA�)o��n9*}Zc.cie]jsh)g�nlh?bGokcfe?r3e?bk��r^okq.h}´���}8�opnlokbd±?osg�cie¥·.e�cfy~osglojµÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3t�²`h)b]j°�e?u{jk}lu{h?b]bdh)g#uwe1q.�)h)bÉr�osqdh�b.o�e?�lq.o�±Kywe?g�}lg#r�hZjkh�osbdjsqdy{�ly~osglnlhUosucfe?�lu{okq.h�okg'cZ�osqdzUy~glh)bxnlo·¸Pr²t�×Åx ç ×4v¡°?Õ���}Abfe?glnAhÇjk}3e?glnAhÇbdo�e�glosjkosb.e?q.y~hÇ��}lo¸Âtm£òx»¸~vNr�£°?ÕA�

ê3ëÍ `ë � ë ¶Ookq.y~Álj�e?qp��}lo%osu`z\�okc.hZnlh¢£¥¤{× £¥¤{ס)¤4à ��¤)¡4à Õ)¤)¡4࣠£¥¤1� �y× £à)¤1�¡)¤{× Õ�¤{îA£ ñ)¢)¤{îA£ ��à1¢�¤{îA£ î�¤*îA£��¤4à ï)¤{×)¢ £�î)¤{×)¢ �yà)¤{×)¢ ��¤*×)¢ ¢��î�¤Z£�ñ)¡ ¢ £�¡4à)¤Z£�ñ)¡ ¢ �ÌîA£¥¤Z£jñ�¡ £�¢)¢�¤Z£�ñ)¡

glh�okb]nlo*h)qdnlosgÛàZ�ê3ëÍ `ëÍ °ë ºAe1�ly{okglnlh���}lo�oku`b.y~�)}ly{okg�cfo�z\�okcfhKnlh�osbÉnlo*h)qdnlosgÇ��j�e?u~js}lu{e?qò¸>�âº

¢¸ ¸º1°1� ¢ º1°1�×VxAº ×±x º xÅtÏ¡{¸�v � � tY¡{¸�v � �£¥¤?Õ ¢ ��¤?Õ £¥¤?Õê3ëÍ `ëÍ&°ë ¬�h)z|rlq.h)�le?qÂu{e?bGjkh)glnly~jsy~h)glosbÂnlo�h?q.nlokg��xr3e?q.e�osu & Õ'�(ÌÖ Ñ Ö P '�& Ò 'RQpTVU ÕW ÓÄÒ (yÖÑ 'rqsk ( Ó�t ' + ¢ ¢ ¢ ¢£¥¤)¡ £¥¤1� £�¤1� ¢£ ¢ £ ¢£¥¤?Õ ��¤?Õ £�¤?ÕÌÎÍ ê3ëÍ °ë ên+`ë a�b.jkq.y{�Ay{q<}Ag�rAq.h)�)q.e?zUe�§BÓV®G��®5��­ ��}lo\e?rlu~y{��}lo"oku�z\�okcfhKnlhbdosz|y{o�µZrluÏ�� jky~cfh�nAo3á�}Zcfji¦lokqpe%okjs}3e1jsy{h?glosb8osb.jse?uwe1q.osb:u{y~glo�e1u{osbk��osb8nlosjky{qs��nlo5uwe�ÄÅh)qdz�el�m7r5u � tL�]vylVovu q t��]vpjkh)gau � zRu q t{§ x]¾ §��

£)£

Page 20: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÌÎÍ ê�ëÍ °ë ê�ê�ë a�b.jsqdy{�ly~q�}lg�rAq.h)�)q.e?zUe�§BÓV®G��®5��­ ��}lo�n3e1nlh�osuBcie?�Au{osqdh�nlo�}Agz\�okc.hZnlh�nAosjsy~n3e�b.y`osbÉnlo*h)qdnlosgÛàZ�ê3ëÍ&`ë ê3ë ¬�h)gAb.y{n8�osq.okglb.o�u~h)b'�e?qd�^h)u~osbxnAo·ªxwOy�okc.y{��}lo�cie?nlh?b�jsh)g'u{h?bxosg�cfokq.h)b*nlo�£e<z%jsh?g�osuPh?q.nlokg�¦3e?�lyªcf}3e?uY�va�bdc.}lnly{e?glnlh�u~h)b8±1e?u~h)q.okb�r�h)b.y~�lu{okb���}loxrA}losnlokg�cfh)zUe?q�6tY¡4vÄz�6t�×�vÄz� j j 6zZ�6t�z4vÑ�lrlqdh)�3e?qÉ��}lo�¬Èe?q.n?ª�w.yDr�t�z±x+£v�{ê3ëÍ&`ë~ö°ë ºZok�È�}lg�okuZrlqdh)�lu~oszUe]e?g�c.osq.y~h)qB¦3e���bdosy~b��e?qd�^h)u~osbBosg0ª�w " �~®Éosrlqdosbdosg�cie?qdu{h)b�)ql�e1Á3jse?zUokg�cfo��Ônlosjky{q�js}p�e?u{okb�nlo´osu~u{h)b�jkh)q.qdosbdr^h)gAnlosg e�}lg zUy~b.z|h �e?q.��h)uhtÅb.y{go�cfy{��}lo�cie?b�vÈnlo|w " �ê3ëÍ&`ë~ü°ë �5c.y{u~y{Ã�e1glnlh���}lo�¬Èe?q.n¥ª�w.yÂr�t}z±x�£�v�{3n3e?qÉ}lgle|jkh?cie�b.}lr�osqdy{h)qprle?qfe�osug��}lz|osqdh�nlo�jsh)glnAy{jsy~h)glokbxnlo�h)qdnlosg���}lo�nAos��o�bfe1c.y{bdÄ e1jsosq]}lg'z\�o�cfhKnlh�rle?qfe�bdosqxnloh)qdnlosgdîA�~b Ö1( Ô?t:a�u`g��}lz|osqdh�o�µAe?jkc.hUbdo�jse?u{jk}luwe1q3�e�osgÇ}lgÇrlq.h?�lu{okz�e�r�h)bdc.osqdy{h)qk�ê3ëÍ&`ë¤�©ë ¹�e?u~uwe?q�oku��}lgAy{jsh �e?qd�^h)u�nAoJwOy�jkh)g���tL��v(r8z��'osb.jkq.y~�ly{q%osuOnlyªÄÅosq.okgljsy{e?uoku{osz|osg�cfe?u°jsh?q.q.okb.r�h)glnly~osg�cfo*��u{e�jsh)glnAy{jsy��h)g�nlo*h)q.nAosg°�ê3ëÍ&`ëÍ�°ë ´�a�b�y{g��?osjkc.y~±1e<r3e1qfe<cfhKnlh�z<uwe�ÄÅ}lgljky��h)g�� t�wOyâx]¾ �3µ ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3t»Âe?qfe_z0ß���glh|¦3e���jsh)g�c.qfe?oE·dosz|rlu{hl�ê3ëÍ&`ëÍ�°ë ¬�h)glb.y~nlosqdosz|h)b�okuPrlqdh)�lu~oszUe��ly~nly{z|osglbdy{h)gle?u1t�l��Úz�lnqÐvym7rÙtm£4z�uHv�jsh)ggu0ru�t�l��Úz¡l7q�v��e�vB¹�e?u~uwe?qB}lg��e?qd�^h)uKnloÈh?q.nlokghà�jsh)g���tL��v�r¹×)¢]��h?cfqdh�jsh)g���tL��vNr ��¢]��osb.jkq.y~�ly{qu{e?bpnly~ÄÅokq.okgljsy{e?u{okbÈosu~osz|osg�cie?u~osbpjkh)q.qdosb.r�h)glnAy{osg�c.osb]e?u`rlq.h?�lu{okz�e�nloku`osg�}lgljkywe?nAhl��Iv�Æxoknl}ljsy~q�nloku�e?r3e1qdcie1nlh\e?g�cfokq.y{h?q���}lo�r3e?q.e>osbdc.o#cfy~r^h>nAo�rlq.h)�Au{oszUe?bUuwe?bjkh)glnly~jsy{h?glosbpnlo*h)qdnlosgÛà�b.h)g�b.}ZÁ3jsy~osg�cfokb�r�osq.h�glh|b.h?g�glokjsokbfe?qdywe?bk�j�vN´�»Bh)q���}��oposu3e1r3e?qdcfe?nlh�e1g�c.osqdy{h)qvgAh�jsh)g�cfq.e?nly~jsoposuZcfosh?q.oszUexjsh?q.q.okb.r�h)glnly~osg�cfotÅnlo}á�}Ac.ji¦losq�vÉeMÁ3q.zUe?glnlh��K}Ao%}AgÇzÊ�okc.hZnAh�osbpnlo�h?q.nlokg Ê bdyP��bl�h)u{h�bdy°b.o�jk}lzUrAu{osgu{e?bpjsh)gAnly{jky{h)glokbpnlo*h)q.nAosgIµÁ ê3ëÍ&`ë � ¹�e1u{uwe1q�}lg3eÇÄ1�h?q.z�}lu{e�r3e?qfe�uwe�nlokq.y~±1e?nle¶¢1x��okb.y{zUe�nAoUu{eÇjkh)zUr�h)bdy{jsy��h)gnlo�nAh)b�ÄÅ}lgljky{h)gAosbh| zRu+t~§Xx]¾ §Ø�"jkh)z|rlq.h)�le?q.u{e<r3e?q.e#u{h)b�j�e?bdh)b·¢¹r £4zÑ¡7z�×A�ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3tǺZy{z|rlu{okzUokg�cfoxqdosjs}8�osq.nAosb.o�uwe�Ä1�h)qdz�}luwe�nlo%§�e��e�nAy�á�q.}lgAhl�ê3ëÍ&`ëÍ °ë ºZose O yDr ¬Èe?qdnwOys�

£¥¡

Page 21: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

e�vpºZ}Ar^h)gAy{osgAnlhUjkh)glhKjsy~nlh���}lowtÅr3e?q.e0�â¾ ¢�vO � o O q �.oã�����Äo OM� � � � � r�tУex��]v �j�V� tm£�xA� q v �j� � ������tУexA� � v �j�!� oAÆ¥tL� � � � vÄznloknl}ljky{qÉb.y~gÇgAosjsokb.y~n3e?nÇnlo*nly{�l}¥·.e?qpgly{gA�È�}lg �e?q.��h)uO � r £{z O q r�£4z O ÷ r ¡7z O " r �z OM� r¿ñ7z OM� r ¡?¢H ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3tËa�z|rlu{ose?q*r3e?q.eÇu~h)b�j`�e?u~js}lu~h)b?tm£±x��4v � � rå£eo5�±o5� q o�� ÷ oÝ j j ��tУex��4v �j� r&£Âoa¸���oaÆwt��*q�v���Iv�²©e�u~y{bdcfe�e?g�c.osq.y~h)q�jkh)g�cfy~gx�}3e�jsh?g Or� r���îU� OM� r £?£àZ�(´¥¬�}É�e?g�cie1b�jsh)glnAyª�jky{h)glokb�nlo�h)q.nAosg´nlos��o�bfe1c.y{bdÄ e1jsosq�}Ag´zÊ�okc.hZnAh�nloh®5}lgA�)o��n9*}Zc.cie�r3e1qfe�b.okq%nAo�h)qm�nlokgÛî4µ

�4� ê3ëÍ&°ëÍ& Æxosz|h)bmcfqfe1qpuwe�Ä1�h)qdz�}luwe�nAosu©e?r3e1qdcie1nlh|e�v�nlosu`oE·dosqdjsy{jky{h|e?g�cfokq.y~h)qs�ÌÎÍ ê3ëÍ&`ë ê�+`ë a�bdjsq.y~�ly{q5}lg#rAq.h)�)q.e?zUeU§BÓV®G��®É�x­ ��}lo�e?uBy{g�cfqdhZnl}Ajsy{qÉ}lg��e?q.��h)unlo�h)q.nlokgÇÕ���}lg�cfe?�lu{okq.hl�Knlokjsy{nle�bdyPbdo�js}lz|rlu{o�uwe�jkh)q.qdosb.r�h)glnAy{osg�c.o�jsh)glnAy{jsy��h)g�nloh)qdnlosgP�ê3ë ên+`ë ê3ë »�q.h)�le?q���}lo�bdy�o�µZy~bdcfy~osq.e#}lgÊz\�o�cfhKnlh#nlo�h)q.nlokg�£�¢#o�µZrluÏ�� jky~cfh�nlo#£�¢o�cie?r3e1b5jkh)gd¼ � �sr�£*osg�c.h)gljsokb�bdo%nAos��osqs�� e�js}lz|rlu{y~qÈzUeMµutÐ� �C��� � �¡� vsÀ�¢ m £�îZ�ê3ë ên+`ë~ö°ë �]b.e?glnlh´u{h)b�±?e1u{h)qdosb�z|osgljky{h)gle?nlh)b�okgË}lg\rlqdh)�lu~oszUe�e?g�cfosqdy{h)q�r3e?qfe¬Èe?qdn�wOy�jsh?g�£ãß�zÈßùîA�p¦3e?u~uwe?q�oku�g��}lz|osqdh"nlo#okjs}3e1jsy{h?glosb��Ënlo#y~glj`�h?�)gly~cfe?b��}lo�c.y{okglosg�u{e?b�jkh)glnly~jsy{h?glosb]nlo�h)qdnlosg�jkh)q.qdosb.r�h)glnAy{osg�c.osb*e�}lg�z\�okc.hZnlhUo�µZrluÏ�� jsyªcfh�)okg8�osqdy{jkh�nlo�E�okcfe?r3e?bk�*Æxosnl}Ajsy{q]nlosuÂq.okb.}luªcie?nlh�jk}É�e?u~osb�bdh)g�u{h?b]±1e?u{h?q.osb]g3e1c.}lqfe?u~osbnlokuAz��� gly~zUhÉnlosEprle?qfe�jse?n3e�£(ß�z�ß�îA�~´�»Âh)qv��}8�o�osbdc.h�glhxrlqd}los�lexq.y{�?}lq.h)b.e?z|osg�cfou{e?bp�3e?qdq.osq.e?bÉnlo(á�}Ac.ji¦losq�µê3ë ên+`ë~ü°ë ºK}lr^h?gl��e?z|h)bG}Ag|zÊ�okc.hZnAhxnlo�®É}lgl�)oÑ�:9�}Ac.cfe�o�µZrluÏ�� jky~cfh�nloph)q.nAosghà�jsh?gbdosy{b]okcfe?r3e?b5��cfe?uÂ��}loÅ� �n� r�¢A��ÆxokzUh?bdcfq.e?q5�K}Ao0¼ � � � " o�¼ � � � " Ãr&¢A�VÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3t¹]e?u{u{e?q�u{e�jsh)glnAy{jsy��h)g�nlo*h)q.nAosgÇjsh)qdq.osbdr^h?glnly{okg�cfo�e?u*�e?qd�^h)uPu{y{gAo�e?uY�ê3ë ên+`ë¤�©ë �Âq.e1cie1q<nlo>oѵZrlu{y~j�e?q�r^h)q���}��oÊosg�u~h)b�cfe?�lu{okq.h)b���}loÊb3�h)u~h�y~gljsu~}A�)okgg��}lz|osqdh)b�q.e?jsy~h)g3e?u~osbk�Zu~h)b�nlokglh)z|y{g3e1nlh)q.okbÈh�e?u^zUokglh)bÈbd}lbÈÄ e?j�cfh)qdosbpb.}Aosu{okg�e?r3e?qdo��jkosq%q.osr�okc.y{nlh?bs��¬�h)gAjsq.o�cie?z|osg�c.o?�N´�r�h)q*��}��o�okg"u{h?b.¼ ¬ glh<e?r3e?qdosjkoUg�}lgljse<}lg³nlo��glh?zUy~g3e?nlh)q�glh�cfq.yª±Kywe?u^�K}Ao�bdo�e�jsh)rlqdy{z|h�jsh)g�u~h)bpnlosz��e?b�µ

£�×

Page 22: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ê3ë ên+`ëÍ�°ë Æxosz|h)bdc.qfe?q���}lo�b.yÈokgË}lg\z\�okc.hZnlh�nAo�®5}lgA�)o��n9*}Zc.cie#oѵZrluÒ�� jsy~c.h#jsh?gc.hZnlh?bxu{h)bG@��OnAy{bdc.y{g�cfh?b�osuGh)q.nlokg'jsh)y~gljsy~nlo�jkh)g'osuGg��}AzUokq.h�nlo�o�cie?rle?bYE)�°osg�cfh?gljsokbu~h)b�@��pnlo�cfosqdzUy~g3e?gÊu~h)b�¼��E�´a�gÊr3e?qmcfy{jk}luwe1qs�vjkh)glhKjsy{nle O b3�h?u{h#¦3e��"}lgÊr^h?b.y{�Au{o \¼¥�ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3t�¬�h)glbdy{n8�okq.osgAb.o%uwe?bÈjkh)glnly~jsy~h)glosbpnAo%h?q.nlokg�z}r�£4zÑ¡7zj T j 6z�E*jkh)q.qdosb.r�h)gZ�nly~osg�cfokb5e?u%�e?q.��h)u°��}lo*jk}lzUrAu{or��tL��v�r�zK�ê3ë ê�ê3ë ê3ë ¬�h)glbdy{n8�okq.okb.o%osu`z\�okcfhKnlh�js}Z�)h�cie?�lu~osqdh|okb

¢ £ ££ £�¤)¡ £¥¤?¡×)¤?Õ £¥¤1Õ ¡)¤?Õe�vÈ»�q.h?�3e?qÉ��}lo*osb5nlo*h)q.nlokg#¡���gAhUokb5nAo%h?q.nlokgÛ×�osgÇ�)okglosq.e?uÏ��Iv%»Oqdh)�3e?q���}lo�b��� osb�nAo�h)q.nAosg ×<rle?qfe�c.hZnle?b�u{e?b�okjs}3e?jky{h)gAosb�u~y{glose?u{okb%nAo�uweÄÅh)qdz�e�l m r��Èl�nlh)glnlo�� osb5}lg3e�z�eMcfq.y~Ã�nlo%jsh?glbdcfe?g�cfosbk�ê3ë ê�ê3ë~ö°ë »�q.h)�3e1q5��}lo�b.y©osg�osu©rlqdh)�lu{okz�e�e?g�c.osq.y~h)qÈcfhKnlh)b5u{h?bposu{okzUokg�cfh)b5nlo<�bdh)g'gK}Au{h)bxoѵZjsosrZcfh�� ��q ��� q ÷ ��� ÷�" �`osg�cfh?gljsokb%okuvh)qdnlosg'nlokuvz\�o�cfhKnlh�okb%�A��´�­]hjkh)g�cfqfe1nly{jko]okbdcfh�osu3cfokh)q.okz�e%�K}Aoxe1Á3qdz�e1�3e%��}lo]}lg�zÊ�okc.hZnAh�oѵArAuÒ�� jky~c.h�nloGE�okcfe?r3e?bc.y{osgAo*e|u~h�z+�e?bph?q.nlokg Eµ�4� ê3ë ê�ê3ë{ü ¹�e1u{uwe1q8}lg�z\�okc.hZnlh���}lo�bdo�e�nlo�h)qdnlosg���r3e?q.e�osjk}3e?jsy~h)glokbposb.jse?uwe1q.osbnlo*u{e�ÄÅh)q.zUe�l m r¿|~t�lHv:��glh|u{h�bdo�e�osgÇ�)osgAosqfe1u`r3e?qfe�b.y~bdc.oszUe?bs�ÌÎÍ ê3ë ê�ê3ëè�©ë ¬�h)z|rlq.h?�3e?q*g�}lz\�okq.y~j�e?z|osg�cfo���}loUosuOz\�o�cfhKnlh�nlo|h)q.nlokgÊ¡Çe?g�cfosbjky~cie1nlh*jsh)g�±)okq.�)o]z+�e1b:ql�e?rly~nlh*r3e?qfe�bdy{bdc.oszUe?bOu{y~glo�e?u~osb�jkh)gUjkhZo�Á3jsy~osg�cfokb�jkh)glbdcfe?g�cfokb��}lo*r3e?q.e|h1cfq.h?bprlq.h)�Au{oszUe?bk�ê3ë êZö°ë ê3ë ºZ}Ar^h)gA��e?z|h)bv��}loÉosg�}lg�rlqdh)�lu{okz�e�e1rlq.h�µZy{zUe?z|h)b�l�t�¼ÄvÂ}lb.e?glnlh%b.}Ajso��bdy~±1e?z|osg�cfo:r3e?bdh)bN¯°��¡4¯��%��¯°�vºZo�e?g<� > �,� qn> �,� " > u{h?bÂqdosb.}Au~cie1nlh)bGh?�Acfokgly{nlh?bs�v»�qdh)�3e?q��}lo*r3e?q.e¥¯�b.}AÁljsy{okg�cfosz|osg�c.o�r�os��}lo� glh�oku`h)q.nlokg Ê nloku`z\�o�cfhKnlh�±)osqdy~Á3jse

Ê]¡ u~h)�|X�� " > x�� qn> XÂx"u{h)�|X�� qn> x�� > Xu~h)�8¡ê3ë êZö°ë~ö°ë ��uOe?rAu{y{jse?qxjky{osqmcfh�z\�okcfhKnlh�jkh)g³nAy~ÄÅosqdosg�cfokb�rle?b.h)b*bdoU¦3e�h)�Ac.osgly~nlh�uwecfe?�luwe

£��

Page 23: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

¯ l{½¢ m £¥¡4à × m ×)¢)Õ�ï*î4×?�)�¢*m ¢)Õ�¡4à ×*m ×A£�Õ�à*î�ï1��à¢*m ¢4×A£¥¡{à ×*m ×A£�ñ�¡1¢4ñ�à{î¢*m ¢A£à?Õ)¡4à ×*m ×A£�ñ4î{î)Õ�¡Z£e�vÈa�bdc.y{zUe?qposu`h?q.nlokg�}lb.e?glnlh|uwe�Ä1�h?q.z�}lu{e�nlosu`rAq.h)�lu~oszUe�e?g�cfokq.y{h?qs��IvO�5c.y{u{y~Ã�e?qGuwe*o�µKcfq.e?r^h?uwe?jky��h)g�nlo/®5y~ji¦3e?qdnlb.h)gUr3e?q.e%okbdcfy~z�e1q:oku�osq.qdh)q:jsh)z|okc.y{nlhokg�u~h)bÈcfqdosb'�}lu~c.y{z|h)b:±1e?u~h)q.okbs�ê3ë êZö°ë~ü°ë a�g�osu^rlq.h?�lu{okz�e�e1g�c.osqdy{h)q8uwe�bdh)u{}ljky��h)g�q.o�e1uPosq.e0× m ×)¡?¢A£)£�Õ{ñ�¡{×ò j j i�Oa�bm�c.y{zUe?q�nlo*g�}lo�±)h�oku°h)q.nAosgÇ}lbfe?gAnlh�e?¦Ah)qfe�osbmcfo*n3e1c.hl�ê3ë êZö°ë¤�©ë e�v�a�bdjsq.y~�ly{qUuwe³Ä1�h?q.z�}lu{e³jkh)q.qdosb.r�h)glnAy{osg�c.o'eÊe?rlu{y~j�e?q|osu]z\�o�cfhKnlh>nloa�}lu~osqpnlh)bp±?osjsokb�jkh)g�rle?b.h¥¯I°)¡Z��Iv5�]bfe1q�uwe�y{nAo�eUnAo�®Éy{ji¦3e?qdnlb.h?g#r3e?q.eUjsh?z��ly{gle?q5e�vÉjkh)g#okuÂz\�okc.hZnlhUnlo�a�}lu~osqnlo*r3e1b.h¥¯`�Ah)�Acfokgly{okglnlh|}lgÇz\�o�cfhKnlh�nlo*h)q.nAosg<¡Z�D´M¨x}8�o*z\�okc.hZnlh�okbÚµê3ë êZö°ëÍ�°ë aGµZrlu{y~j�e?qUj`�h)z|h"}Zcfy{u~y{Ãse?q�osu]rlq.hKjsoknly{z|y{okg�c.h³nAosu�rAq.h)�lu~oszUe³e1g�c.osqdy{h)qr3e1qfe�nlosz|h)bmcfqfe1qx��}lo�¦3e���z\�o�cfhKnlh)b�nlo·®É}lgl�?o��:9�}Acdcie�o�µZrluÏ�� jky~cfh?bxnlo�h)q.nAosg´e?q.�Ayª�c.qfe?qdywe?z|osg�cfo��)qfe?gAnlo?�?´�»Âh)q���}8�o|osbmcie�jsh)gAbdcfqd}ljsjky��h)g´glh�osb%nlokz�e?bdywe?nAh��}Zcfy{uÂosg´uwerlql�e?jkc.y{jse�µê3ë êZö°ëÍ�°ë »Âe?qfeUosuGrAq.h)�lu~oszUehl m t��]vòr�l��^jkh)g�l�tY¢�vÂr £)�^osuBz\�o�cfhKnlh�nlo�®5}lgA�)o��9�}Acdcie�o�µZrluÏ�� jsyªcfh�nlo*jk}3e1cfqdh�okcie1r3e?bÉnlo*cie?�lu~osqdh

¢£°)¡ £°)¡x%£ £°)¡ x3×�°?¡£ ¢ ��°{× x�£�°{×£¥¤?Õ ¡)¤{× ¢ £¥¤1Õ¦3e�rlqdhZnl}Ajsy{nAh|u{e�b.y{�?}ly{okg�c.o�cie?�lu{e�nlo*osq.qdh)q.okb�e1u©e?rlq.h�µZy{zUe?qpu{e�bdh)u{}Ajsy��h?gÇokg�jky{okqdcfhrl}Ag�c.h ¯ osqdq.h)q¢*m × £Tm ¡*î4î�à?Õ±��£�¢ �¢"¢*mw£à ñ*m ¡M�l£�×4×±��£�¢ � �¢*m΢�ï4à à#m¤ï{ï?Õ4×4ñ±��£�¢ � �¢*m΢4×�ï4à ×*m¤ïM��ï4à{î±��£�¢ � �

£à

Page 24: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

e�v�Æxo�cfokq.z|y{g3e?q5osuÂh)q.nAosg#cfo°�h)q.y~jsh�nlokuGz\�okc.hZnlh�}lbfe?gAnlh �e?q.��h)u~osbxnlo�á�}Acfji¦Aosqx�¦3e1u{uwe1q�osu`h?q.nlokg�okzUr°�� q.y~jsh�osz|rlu~o�e?glnAh�uwe�cie?�Auwe�e?g�cfokq.y~h)qs��IvpaGµZrlu{y~j�e?qpu{e�nly{bdjsq.okr3e?gljkywe�osg�c.q.o�e?z���h)bpq.okb.}luªcie?nlh?bs�ê3ë êZö°ë � ë »Âe?qfe�}lg�z\�o�cfhKnlh�nlo±®5}lgA�)o��n9*}Zc.cie�b.oxh)�Zcfy{okglo�u{e�b.y~�)}ly~osg�cfo5cie?�lu{e�nlookq.q.h?q.osb ¯ okq.qdh)q£�°Z£)£ ¢#m΢�¡{×4à{×£�°Z£¥¡ ¢ m ¢A£ï1¢4×£�°Z£�× ¢ m ¢A£¥¡1Õ�¡£�°Z£�� ¢ m ¢)¢4ñ4à4à

¯ osqdq.h)q£°Z£à ¢*m΢?¢�ï{×)Õ£°Z£�Õ ¢ m ¢?¢�à4ï4Z£ï ¢ m ¢?¢?��à{Z£�î ¢ m ¢?¢4×)Õ4îÆxoknl}ljsy~qposu`h)qdnlosgÇnloku`z\�o�cfhKnlhl�

ê3ë êZö°ëÍ °ë ºZ}lr�h)gl�)e?zUh?b:��}lo]¦losz|h)b:rlq.h?�)qfe?zUe?nlh*}lg|z\�okcfhKnlh%nlo/®5}lgA�)o��n9*}Zc.cie��}loÉe?rAq.h�µZy{zUe/l�t�¼ÄvBr3e1qfe�e?u~�È�}lg�rlqdh)�lu~oszUe]osbdj�e?u{e?qG��z�}lokbdcfq.exosg�r3e1g�cfe?u{u{e]okulosqdq.h)qjkh)zUo�cfy~nlh�b.y~g�±?e1u{h)qpe1�lb.h)u~}AcfhA�OºZy`e?uPq.osnA}ljsy~qposu`r3e?bdh�osu°okq.q.h?qpb.o�±1e�qdosnl}Ajsy{okglnlh��okg�e?u~�È�}lg�zUh)z|osg�c.h%jse?z��ly{e%nAo]bdy{�)glhA�KoѵZrlu{y~j�e?qOr�h)q8��}8�o5rlqdh)�3e?�lu~osz|osg�cfo5osbmcfokzUh)b±Ky{okglnlh�u{h?bposq.qdh)q.okb]nAo%qdosnlh?glnloshA�ÌÎÍ ê3ë êZö°ëÍ&°ë aObdjsqdy{�ly~q]}lg<rlq.h)�?qfe?zUe�§ÂÓV®G��®É�x­���}lo�e?rAu{y{��}lo%}lg#zÊ�okc.hZnAhUnloh)qdnlosg\×�jkh)g'rlq.okjsy{bdy��h)g�bdy{z|rlu{o�e�}lg'rlq.h?�lu{okz�e�nAosuv��}lo�b.o�jkh)glh)Ãkj�e�uwe�bdh)u{}Ajsy��h?g°���z�}losbmcfqdo%}Ag3e�cie?�lu{e�jsh?gÇoku°osqdq.h)qpokg�ÄÅ}lgljsy��h)g�nlo(¯°���Âq.e1cie1qpnlo�nlosnA}ljsy~qÉe�rle?qdc.y{qnlo*��}8�o.¯�y~g!£3}A�?osg<u~h)bÈokq.q.h?q.osb5nlo*q.oknlh)glnAoshl�ÌÎÍ ê3ë êKö`ë ê�+`ë a�uwe?��h)qfe1q:}Ag�rlqdh)�)qfe1z�e*§BÓV®G��®5��­ ��}loxe%r3e1qdcfy~qOnlo�}lgle%cie1�luwenlo*r3e1b.h)bp��okq.q.h?q.osbÉokbdcfy~zUo�oku`h)q.nAosgÇ}lbfe?gAnlhUqdos�)qdosbdy��h)gÇu{y~glo�e?uY�ê3ë êZü°ë ê3ë �]uPcfh?z�e?q:nlh)bprle?b.h)bpjkh)g¶¯wr ¢*mw£x��}lglh�jsh?g�¤ ¯wr ¢*mΡ�osg�}lg�z\�okcfhKnlhnloÇh)qdnlosgã×A�Èh)�Ac.osglokzUh?b?l q r ¡#mw£�ï1��àZ� ¤l q rø¡mw£à?¢{îA�ÔºZy5e?nlz|y~c.y{z|h)b�}lgËosqdq.h)qz��eMµZy{z|h�nlo�¡±��£�¢ �n÷ ��´���}8�o%r3e?bdhUnAos�ly��osqfe1zUh)bÈc.h)zUe?qÚµê3ë êZü°ë~ö°ë ¬�h)glb.y~n8�osqdosbdo�osuBrlq.h?�lu{okz�e·lnm�rpl(oËb.okg�tL�IlHv�� lut ¢�vDr £)�5¬�h)g#e��K}lnlenloÉ}lgle*jse?u{jk}luwe1nlh)qfe�e?rlu{y~j�e?qGosu3z\�okcfhKnlh�nlo5a�}lu~osq�jsh?g¥¯¥r ¢*mw£Éjse?z��ly{e?glnlh�okulr3e?bdhr�h)qvz|osnly~h�nlopo�µKc.qfe?r�h)uwe1jsy��h?g�nloe®5y~ji¦3e?qdnlb.h)g�jkh)g|}lg�osq.qdh)qvu~hZjse?uZc.h)u{okqfe?nlh�nAoÉ¢*m΢A£��}AgÇÄ e?j�cfh)qpnAo%bdos�)}Aq.y{nle?nÇ¢*m ñA�8¬�h)g�c.y{g�}3e?qpu~h)bpj`�e?u~js}lu~h)bp¦3e?bmcie���}loV� � À�¢*m ×1�l�

£�Õ

Page 25: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÌÎÍ ê3ë êKü°ë{ü°ë a�b.jkq.y~�ly{qp}lg�rlq.h?�)qfe?zUe�§BÓ}®Â��®5��­&��}lo�q.ose?u{y~jso�u{h?b5j°�e?u{jk}lu{h?bpnlosurlqdh)�lu~oszUe�e?g�cfosqdy{h)qk�ê3ë ê��©ë ê3ë ¬�h)glbdy{nlokqfe?z|h)b�okuÈr3e?q�okglj�e�·.e?nlh'nlo�cfqdosb�okcfe?r3e?b�jk}A�)h?b��}Agly{jkh)b�osu~o��z|osg�cfh?b�glh�g�}lu~h)b�bdh)g¥@ q r�� q¡� rÿ£°?¡Z�.@ ÷ r�� ÷Ì÷ r�¼ q rÿ£?�C¦ ¼ � rÿ£°1ÕA�§¦ ¼ q r ¡{°{×A�¦ ¼ ÷ r £°?ÕZ�³¹]e?u{u{e?q%osuÈh)qdnlosgÊnAo�e?z���h)b�z\�okc.hZnlh?b��>bdoK g3e?u{e?q�bdy�b.h?g�oѵZrluÒ�� jsy~c.h)b�hy~zUrluÏ�� jky~cfh?bs�]b Ö1( Ô?t�a�g>osuOqdosbdc.h#nloUu{h)b*rlqdh)�lu{okz�e1b%bd}lr�h)glnlqdosz|h)b���}lo|cfhKnlh)b%u{h)br3e1q.osbÉokglj�e¥·.e1nlh)b5b.h)gÇo�µZrluÏ�� jsyªcfh)bk�ê3ë ê��©ë~ö°ë ¬�h)glbmcfqd}ly{qpcfhKnlh)bpu~h)bpr3e?qdosbÉosgAj�e¥·.e?nAh)b�£�tÏ¡4v�jkh)g�nlh)bÉokcfe?r3e?bk�ê3ë ê��©ë~ü°ë aGµZrlu{y~j�e?q�r^h?q���}8�o�bdy�osgÊ}Ag>r3e?q�okglj�e�·.e?nlh#nlo]E�o�cie?r3e1b�� A �er²¼��È�¼ A r&¢|osg�cfh?gljsokbxb.o%q.oknl}ljso�osu©gx�}lz|osq.h|nlo%h)r�osqfe1jsy{h?glosbk�ÉaOgAjsh)g�cfq.e?q�u~h)bÉz\�o�cfhKnlh)bnloku`rlq.h?�lu{okz�e�e?g�c.osq.y~h)qp��}lo*bfe1c.y{bmÄ e?jsokg�okbdcfo%q.ok��}losqdy{z|y{osg�c.hl�ê3ë ê��©ë¤�©ë ¹]e?u{u{e?q%e?u{���}Ag´rle?q�okglj�e¥·.e1nlh#nlo|cfy{r�h´£�tÏ¡4v�jsh?g"cfqdosb�o�cie?r3e1b�bfeMcfy{bmÄ eM�jky{osgAnlhh� ÷ �urȼ��©��¼ ÷ r ¢A�ê3ë ê��©ëÍ�°ë ®Éosr�okcfy~qÂoku�rlq.h)�Au{oszUeÉosg�}lgljkywe?nlh�e?g�cfokq.y{h?q.z|osg�cfo:osg�oku��K}Ao�b.o8osz|rlu{oseM��3e�o�µKcfq.e?r^h?uwe?jky��h)g³nloâ®Éy{ji¦3e?qdnlb.h?g\e?rlu{y~j�e?nle<eÛl�mZr l0o bdosg�tL�IlHv%rle?qfe<jse?z��ly{e?qokuvr3e?bdhl�`r^okq.h�}lb.e?glnlhÇe?¦Ah)qfe�okg´bd}'u{}l��e1q�}lg'r3e?q�okglj�e�·.e?nlh'£�tÏ¡{v���¬�h)zUrle?qfe?q]osuc.qfe?�3e�·dh|jkh)z|rl}Acie1jsy{h?g3e?uPokg<e1z��^h?bpj�e?bdh)bs�ê3ë ê��©ëÍ�°ë »�q.h)�le?qÉ�K}Ao

¢£�¤1� £¥¤M�£�¤)¡ ¢ £¥¤)¡£ £ x�¡ ¡£ x�¡ ¡ ¢£¥¤1Õ ¢ ��¤?Õ £¥¤?Õokb5}Ag�r3e1qposgljse¥·.e?nlh�¡t ��vÑ�

ê3ë ê��©ë � ë ¹�e1u{uwe1q8cfhKnlh)bÉu~h)bpr3e?qdosbÉosgljse¥·.e?nlh?bx¡t�×�v8nlo%uwe�ÄÅh?q.zUe

£ï

Page 26: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

¢ £ ££¥¤?¡ � ÷ � � ÷ q¼ � ¼ q ¢¦ ¼ � ¦ ¼ q ¦ ¼ ÷ÌÎÍ ê3ë ê��©ëÍ °ë �]b.e?glnlh�e1u{���}lg*r3e?qBosgAj�e¥·.e?nAhl�)osu{e?��h)qfe?q©}lg�rlq.h)�?qfe?zUe]§BÓV®G��®É�x­��}lo�e?rlu{y~��}loOosu�jsh)qdq.okb.r�h)glnly~osg�cfo8z\�o�cfhKnlh]nAo8r3e1b.h]±1e?qdywe?�Au{o:eel m r jkh)b�t��]°tm£4oÅl q v�v��l�tY¢�v�r ¢�jsh)gÇ}lg3e�cfh)u~osq.e?gljsy{e�nlo%¢ m ¢?¢)¢A£�osgÇosu`okq.qdh)qÉu{hKj�e?uY�9�Ü :=< â¥>)@sàÅB é�ä äGáDC6Eö°ë ê�ë ê3ë ¬Èe?q.e?jkc.osqdy{Ã�e1qposu°±1e?u{h?qÈnlo*uwe�jsh?glnly{jky��h)g�y~gly{jkywe?u]lut ¢�v8okg�oku`rlq.h)�Au{oszUe

l m r ì x3à x5�¡ £¥ð lr3e1qfe���}lo�e1u`e?rlu~y{j�e1qÈosu`z\�okc.hZnlh�nAo�a�}lu~osqÉjsh?g�¯?r £*b.o%js}lz|rluwe�u~y{z»l � r ¢A�

ö°ë ê�ë~ö°ë »�q.h?�3e?qOosu3cfokh)q.okz�e*nlo5u{h)b�j?�� qdjs}lu~h)bOnlox¾�osqdb.¦l�?h)q.y~g|��}lo�e1Á3qdz�e���}lo5u{h)be?}Zcfh�±1e?u{h)qdosbÈnAo%}Ag3e|zUe1c.q.y{à O r�t��C� ¬ v�r�osqdc.osglokjsokg�e�uwe�}lgly��h)g�nlo*u{h?bpj)�� qdjs}lu~h)bÈokgoku`rluwe?gAh�jsh)z|rlu{oE·dh�n3e?nlh?b5r�h)qH¨��]r©-1%�t��ª%}x �C������ß�« ¬?¬2 � � �C� ¬ �`/��ö°ë ê�ë~ü°ë ¬�h)glbdy{n8�okq.okb.oÇosuÈrlqdh)�lu~oszUe�l m r O l���lut ¢�v0r`l{��jkh)g O ¦©� q © q t�§Vvnly{e?�)h)gle?u{y~Ã�e?�lu~o�osgÛ§���ÆxokzUh)bmcfq.e?q]��}lo�b.yGu~h)b5osu{okzUokg�cfh)b]nlo O bdh)g�z|osglh)qdosbx��}lo}lgAh�osgDZ1e?u{h)qÉe1�lb.h)u~}Acfh���u{y~z ��­ � 0 lut��]vDr�¢A�3okg�c.h)gljkosb�e?u©e1rlu{y~j�e?qpokuBzÊ�okc.hZnAhUnloa�}lu~osq�jsh)gËjs}3e1u{��}ly{okqh¯ æ £�bdo�jk}lz|rlu{o�u{y~z»l � r ¢A��ÎÄÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3t��5c.y{u~y{Ã�e1q�osuc.osh)qdoszUe�nAo%u~h)bpj?�� q.jk}lu{h)b�nlo�¾�osqdb.¦l�?h)q.y~g°�ö°ë ê�ë¤�©ë ¬�h)gAb.y{n8�osq.okb.o%osu`rlqdh)�lu~oszUe

l m r ì ¡1��¡ ×)¡1�x%£�î4× x�¡1��à*ð l  »�q.h?�3e?qÈ��}lo*js}le?u{��}ly~osqfe��K}Ao%bdo�e�uwe�jsh)glnAy{jsy��h)g�y{gAy{jsy{e?u3��oku°r3e?bdhh¯ æ £)�Ae?u°e?rAu{y{jse?qoku`z\�o�cfhKnlh�nlo%aO}Au{osqpbdo%c.y{okglo�u{y~zal � r u{y~z ��­ � 0 lut��]vNr ¢A�Z´¥¬��h)z|h|okb]r�h)bdy{�lu~oxb.yu~h)bpjshKokÁ3jky{okg�c.osb5b.h)gÇz�}A���)qfe1glnlosb�µ

£�î

Page 27: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÌÎÍ ö°ë ê�ëÍ�°ë a�bdjsq.y~�ly{qG}lg�rlq.h)�?qfe?zUe�§BÓ}®Â��®5��­+�K}Ao5jse?u{jk}lu{o�uwexb.h?u{}ljky��h)g�g�}lz\�o��qdy{j�e�nAo l m ríì x�Õ{î x5�Õ�ï ׶ð l  okg�osuAy~g�cfosqm±1e?u{h�Ü ¢Hzs£TÞKr^h)qGzUoknly{h]nlosuZz\�o�cfhKnlh�nloÈaO}Au{osqGjsh)g·¯¥r ¢*m΢1�l�?rlqdy{z|osqdh�jsh?goku�±1e?u~h)q�y{gAy{jsy{e?ul�tY¢�v�r�tY¢HzTx�Õ4×4v Ë ��nAosb.rA}��osbÈjkh)g¥l�tY¢4v~r�t�x5�ziÕ4ï4v Ë �vavµZrlu~y{jse?qOu{h)bqdosb.}Au~cie1nlh)bs�

ö°ë~ö`ë ê3ë ¹]e?u{u{e?q�oku`nlh)z|y{gly~h�nlo*osbmcie?�ly~u{y~n3e?n�u{y~glo�e1uPnloku`z\�o�cfhKnlhl � � � rÈl � oP¯I|m��� � o ¯

¡ z l � oal � � �¡ �  ö°ë~ö`ë~ö°ë ¬�h?glb.y~n��osqdosb.o�oku�nlh?zUy~gly{h'nlo#okbdcfe?�ly{u~y{n3e1nËu~y{glose?uÉr3e?qfe´osu]z\�o�cfhKnlh"nloa�}lu~osq�z|oзdh)q.e?nlhl��aObmcf}lnAywe?q*b.yGosb*b.y~z\�o�cfq.y~jsh�jkh)g'q.osbdr^okjkc.h#e?uvrA}lg�cfh�%�r x%£Ût osbnlokjsy~qs�ly~g�±1e?qdywe?g�c.oxr^h?qÈ�)y{qdh)bÈnlo�£jî)¢1�]e?u{qdosnloknlh)qÈnAo%nAy{ji¦lh�rl}Ag�c.h�v��3jkh)g�q.okb.r�osjkc.h�eu{e�q.osj�cie�®Ez®%.r ¢A�A��jkh)gÇq.osbdr^okjkc.h�e�uwe�qdosjkcfe?®ÉoK%�r x�£?�ö°ë~ö`ë~ü°ë ºZo�nly{jkoU��}lo|}lg´z\�o�cfhKnlhÇosb.ª�x5osbmcie?�Au{o|b.y:e?uOe?rlu~y{jse?q.u~h�e¶l�m1r « l#b.ojk}lzUrAu{oVl � � � r�¯·t « ¯Iv�l � jsh)g�¯·tL%�v�¾ ¢|jk}3e?glnAh¥®ÉoK%ž xr �e�v°»�q.h?�3e?q`��}loOuweÈqdos�)u{eÈnlosu)c.qfe?r�osjky{hpglhÉosb�ªòx5osbdcfe?�lu~o:z|y{okg�cfqfe1b°��}loOosu�z\�okcfhKnlhy~zUrluÏ�� jky~cfh(l � � � r�l � oP¯I|~tL� � � � z�l � � � v�bs�� u~h�osbs��Iv*aGµArAu{y{jse?q%osg>��}8�oUb.osg�c.y{nlh#u~h)b*z\�o�cfhKnlh)b.ªòx]okbdcie1�lu{okb�y{z|y~cfe?g�zUoE·dh)q%osu:nlo��jse?y{z|y{okg�c.hÊq3�e?rAy{nlh\nlo´uweÊb.h?u{}ljky��h)g nloJlnm�r « l�js}3e?gAnlh¿x/®5o « okb��)q.e?glnlo'okgjkh)zUrle?qfe?jky��h)g�jkh)gÛ¯ � � �ö°ë~ö`ë¤�©ë ¬�h)gAb.y{n8�osq.okb.o%osu`rlqdh)�lu~oszUe

l m rXì x�£�¢ ñ£�¢ x%£)£�ð l  ¬Èe?u~js}lu{e?q�e?rAq.h�µZy{zUe?n3e?z|osg�cfo(tÅjsh)g|}lg|osqdq.h)q�z|osglh?q:��}loÉoku`£¥Ö·v�oku3b.}lrAq.osz|h%nloÉu{h)b¯���}lo%rl}loknlosg�osz|rlu{ose?q.bdo*r3e?qfe���}lo%jsh)gÇjs}le?u{��}ly~osqpjsh?glnly{jky��h)g�y~gly{jkywe?u^u{y{z»l � r ¢A�nlh?glnlo¥l � okb�uweÇb.h)u~}ljsy��h)g"g�}lzÊ�osqdy{jse�h)�Ac.osgly~n3e#e?u8e?rlu~y{jse?q*osu:z\�o�cfhKnlh<nlow®5}lgA�)o��9�}Acdcie�jsu��e?b.y~jsh�nlo*js}le1cfqdhUo�cie?r3e1bÉ��h)q.nlokg�jk}3e1c.q.hl�

ÌÎÍ ö°ë~ö°ë��°ë a�b.jkq.y~�ly{q5}lg<rAq.h)�)q.e?zUe|§BÓV®G��®É�x­&��}lo�jkh)zUrAq.}lok�^o�osu©q.okb.}luªcie?nlhnloku`rlq.h?�lu{okz�e�e?g�c.osq.y~h)qs�

£�ñ

Page 28: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ö°ë~ü`ë ê3ë ¹]e?u{u{e?q�u{e�ÄÅ}Agljsy��h)g�nlo%e?zUrAu{y~Álj�e?jky��h)g�nAosu`z\�okcfhKnlh�nlo%a�}lu~osqÉzUoE·dh)qfe1nlhl�ö°ë~ü`ë~ö°ë Æxosz|h)bmcfqfe1q���}lo'r3e?q.e>}lgÔz\�o�cfhKnlh>nloJ®É}lgl�)oÑ�:9�}Acdcie>jsh?glb.y~bdcfokg�cfo'osunlh?zUy~gly{h%nlo�osbmcie?�Ay{u{y~n3e?nUu{y{gAo�e?u�osbpgAh�±?e1j)�� h�����}lo�oku°h)q.y~�)osg�b.y{okzUrAq.o�r�osqmcfokglosjko�ebd}�jky{osqdq.o�h]e?nl¦lokq.okgljsy{eA�GÆxo�¦Aosji¦lh]r^okqdcfokglosjko�epu{epÄÅqdh)g�cfokqfepnlosu�jky{okq.q.o1�NÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3t¯·t}%�v�r £Do�%/oPÆwt}%{qÐvÑ�ö°ë~ü`ë~ü°ë �]b.e?glnlhUuwe�ÄÅ}lgljsy��h)g<nAo�e?z|rlu~y~Á3jse?jsy��h)g°�Ac.qfe1cfe?q]nAo�n3e1q]}lgleUrlqd}los�3eUnlosuc.osh)qdoszUe��K}Ao�eMÁ3q.zUe?�3e���}lo*glh�¦3e���z\�okc.hZnlh?bÈo�µZrluÏ�� jsyªcfh)b�nlo�h)q.nAosg Ê ��zUokglh)bpnloÊ okcfe?r3e?bÁ ö°ë~ü`ë¤� »�qdh)�3e?qÉ��}lo�Á1·.e?n3e�}lg3e�zUe1cfqdy{Ãxjk}3e?nlq.e?n3e O b.o*js}lz|rlu~o�r3e?qfe�%ž ¢

tL�.xv% O v � � r¹�±o�% O o�% q O q o¹�����o°% � O � oPÆwt}% � � � vÐznlh?glnloÈe1�K}°�� uwe5glh?cfe?jsy��h)g�Æ¥tL% � � �yvBy~glnly{jse]}lgle�z�eMcfq.y~Ã�cie?uK��}lo�cfhKnlh)bBb.}Ab�osu{okzUokg�cfh)bbdh)gÛÆ¥tL% � � ��v��

ö°ë~ü`ëÍ�°ë Æxosz|h)bdc.qfe?q:��}lo�}lg�z\�okcfhKnlh�nAoV®5}Agl�)o��n9�}Ac.cfe�osbpnlo�h)q.nlokgÇ¡�b.y���bl�h)u{hbdyx¯·tL%�v/rÞ£�o�%Vo�% q °)¡±o�Æ¥tL% ÷ vÑ��ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3tʺZo�rA}losnlo�}Ac.y{u~y{Ã�e1q]okuvrlq.h?�lu{okz�ee?g�c.osq.y~h)qpjsh?gÛØhr £)�ö°ë~ü`ëÍ�°ë ¬�h)z|rlqdh)�3e?qp��}lo*osu`zÊ�okc.hZnAh|nAo*cfe?�lu~osq.h

¢£¥¤)¡ £¥¤)¡£¥¤{× ¢ £¥¤{×x�£°*× £°{× £glh�okb]nlo*h)qdnlosgd×���b.y~g�osz��3e1q.�)h¯·tL%4vDr&£Âo°%3o°% q °)¡�o�% ÷ °?ÕA�

� ö°ë~ü°ë � ÆxokzUh?bdcfq.e?q:�K}Aoxr3e?q.e�js}le?u{��}ly~osq Ê À+¡�osb8r^h)bdy{�lu~o]okgljsh?g�c.qfe?q8z\�o�cfhKnlh)b��}lo�glh�bdh)g�nloxh)qdnlosg Ê ��bdy{g�osz��3e?q.�?h�bfe1c.y{bdÄ e1jsosga¯·t}%�vZr�£�od%òod%{qÄ°)¡j{jo������6o%TÉ#° Ê {oPÆ¥tL%TÉ � ��vÑ�ö°ë~ü`ëÍ °ë »�q.h)�3e1qv��}lopb.ylokg�}lg�z\�o�cfhKnlhxnlos®5}lgA�)o��n9*}Zc.cie]nlopnlh)bvo�cie?rle?bv��h?q.nlokgnlh?b5bdo*js}lz|rlu{o}� �Ì� r�£)�I� ��q r ¢A�lokg�c.h)gljkosb�u~y{z�± ­ 0 ¯·tL%�vVÃr ¢Z�ö°ë~ü`ëÍ&°ë ¬�h)z|rlqdh)�3e?qp��}lo*uwe�qdos�)y��h)g�nlo*osbmcie?�ly~u{y~n3e?n�nloku`z\�o�cfhKnlh

¡?¢

Page 29: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

¢£¥¤)¡ £¥¤)¡×�¤1� ¢ ×)¤1�¡)¤{ñ ×)¤{ñ ��¤{ñc.y{osgAo�y{g�cfokq.b.okjsjky��h)gÇglh�±?e1j)�� e�jkh)gÇosu`oзdo*y~z�e?�?y{g3e?qdy{h.®5oH%.r ¢A�� ö°ë~ü°ëYê�+ ºZoseË}lg z\�o�cfhKnlh\nlo�®5}lgA�)o��n9*}Zc.cieÊjkh)glb.y~bdc.osg�cfo´��o�µZrluÏ�� jsyªcfh\bfe1u~±)hr�h)q.��}loh� �Ì� Ãr ¢A�|ÆxokzUh)bmcfq.e?q���}loUbdy�b.}´nlh)z|y{gly~h�nlo|osbmcie?�ly~u{y~n3e?n�u{y~glo�e1uGosb³²`r-#®ÉoK% æ ¢ /�okg�cfh)gljkosb]b.}Çh)q.nlokg�okbÉo�µAe?jkcfe?z|osg�cfo�¡Z�

ö°ë~ü`ë ê�ê3ë Æ�e?nlh�oku`z\�o�cfhKnlh�nlo�cie?�Au{osqdh£ £°)¡ £°)¡£ x�£°?¡ ×�°)¡¢ £

okbdcf}Anlywe?qpbd} O x]okbdcfe?�ly{u~y{n3e1n���cfqfeMcie?qpnlo*nly~�l}M·.e?q�osu`nlh)z|y{gAy{h�jkh)q.qdosb.r�h)glnAy{osg�c.o?�ö°ë~ü`ë êKö°ë a�bdc.}lnlywe1q5bdy`osb O x5osbmcie?�Au{o*osu`z\�okc.hZnlh�nlo�cfe?�lu{okq.h

¢ ¢ ¢£ £°)¡ £°)¡£°)¡ £°)¡ö°ë~ü`ë êKü°ë ¬�h)z|rlq.h?�3e?qpb.y`okb O x5osbdcfe?�lu~o�oku`z\�o�cfhKnlh�nlo�cie?�Au{osqdht�×eo ç ×�v¡°?Õ t�×eo ç ×�v¡°1Õ ¢t�×Vx ç ×{v¡°?Õ x ç ×4°{× t�×eo ç ×�v�°?Õ£¥¤)¡ £¥¤?¡ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3tÊ»Ge?q.e�b.y{z|rlu~y~Á3jse?q�}lg'r�hZjkh�uwe?bxh?r^okqfe?jky{h)glokb�jsh)g�±Ky{okglo�osbdjsq.y~�ly{q}¸ãrt�×/o ç ×{v¡°?Õ���okzUrlu~o�e?qpokg�u~h)bpj`�e1u{js}Au{h)bÈÁ3gle?u{okbp�K}AoŸ�qÂrȸ�x+£°?ÕA�ö°ë~ü`ë ê��©ë ºKoxnly{jkox��}lo�}lg3e�ÄÅ}Agljsy��h)g�qfe1jsy{h?g3e?u�|~tL�]v�rc´?tL�]v�°,µ?tL�]v8okbpuwe_¶ �O����·7õ¹¸� ¶§º ô:�_�#��» ¶ �r¼� t�z7z�z4v �#��½ ¶ �R·,�x� º � ºO¾ õ ¶ ½ bdy:�?qjt}´ÅvÐz��)q�t}µÅv.ß®zU��|~tL�]v±r=ú � oÆ¥tL� q yn� � vÑ�:ºZo�rl}loknlo*rlq.h?�3e?qp��}lo�r3e?q.e�j�e?n3e�z0¦����Acfe?u°e1rlq.h�µZy{zUe?g�cfoxoѵZy{bdc.o���osb�}lgAy{j�eZ�e�vp¬Èe?u~js}lu{e?qpuwe�e1rlq.h�µZy{zUe?g�cfo�nlo%»Âe?n8�o?tÏ¡7zi¡4v�nlo*uwe�o�µZr�h)glokgljsy{e?uÏ��Iv~´¥¬�}É�e1uAosb�u{e5ÄÅ}lgAjsy��h?g�nloÉe?z|rlu{yªÁ3j�e1jsy��h?g%rle?qfex}lg�zÊ�okc.hZnAhxjsh)z|h�okuAnlo5¾*e?}lbdbm�²`os�?osglnlqdo*nlo*nlh)bÉokcfe?r3e?bp��h)qdnlosgÇ��µ

¡Z£

Page 30: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

Á j�vOÆxosz|h)bmcfqfe1q��K}Ao]bdy3}lgUzÊ�okc.hZnAh*c.y{okgloME]okcfe?r3e?b���h)qdnlosg�¡CE)��u{h)b�jkhZo�Á3jsy~osg�cfokbnlo*bd}ÇÄÅ}lgAjsy��h?gÇnAo�e1zUrlu~y~Á3jse?jsy��h)g�bdh)g�g��}AzUokq.h)bpq.e?jsy~h)g3e?u~osbs�ÌÎÍ ö`ë~ü°ë ên�`ë ¬�}3e?gAnlh�}lg3e�jse?u{jk}luwe?nAh)qfe|h�}lg�h)qdnlosg3e1nlh)qxe1rlq.h�µZy{zUe?g<y~g�cfosqdg3eM�z|osg�cfo3ú � �3e?bmcie�jkh)g���}loxu~h�¦le?��e?g�rle?qfe}��¦aÜ ¢Hzfu{h?�:¡#Þ���e���}loVú�¿rÀ �nÁ{qsr ¡1¿�osb�}Agg��}lz|osqdh�o�µAe?j�cfh<okg³�le?b.o�¡Z��a�b.jkq.y{�Ay{q*}lg´rlq.h)�?qfe?zUe���}loUnAy{�l}M·do�okg"nly~ji¦lh�y{g�cfokqm�±1e?u~h�uwe?b]ÄÅ}lgljsy~h)glokb¥� | � tL�]vZxPú � �l�P� | q tL�]v�xãú � �¼�°osbmcfy~z�e?gAnlh�osuvz��eMµZy{z|h�nAo�j�e?n3e}lgle<nlo�oku{uwe1bs�vnlh?glnlo�| � osb�u{e#e?rlqdh�µZy~z�e?jky��h)g´nlo��Âe��Ku{h)q�nlo�h)qdnlosgÊ�#�)| q okb�uwee?rAq.h�µZy{zUe?g�cfo*nlo�»Âe?n8�owtm£Âoa�]°)¡eoP�IqаZ£¥¡4v�°tm£�x �]°)¡eoa�IqÄ°Z£¥¡{v��ÉÆxosjky{nly~qÉjs}É�e?u©nlookbdcie1bve?rlqdh�µAy~z�e1jsy{h?glosbBosbÂzUoE·dh)qB�%jk}É�e?g�cie?bÂjsyªÄÅqfe?bBb.y~�)gly~Álj�e1c.y~±1e?b©nlo�u{e5oѵZr^h)gAosgljkywe?url}Aosnlo%n3e?qk� Q�Ü R CTS�à < à�ç�UVCsé�äXWÊç\C�áOé�äü°ë ê�ë ê3ë ºZose|oku`rlq.h?�lu{okz�e�okg�}lgle|nly~zUokglb.y��h)g

å m m rp| å�t��nvZr�å1t�¼Äv�r ¢H �]rlu{y~j�e?qUosuxz\�okc.hZnlhÊnAo�nly~ÄÅokq.osgAjsywe1b�Á3glyªcie?b�rle?qfeÊq.oknl}ljky{q.u~hÊe>}lgÔb.y~bdc.oszUe>u{y{gAo��e?u O \ r \¼¥� ¬�h)z|rlq.h?�3e?q���}lo'nlo�c#t O vãÃr ¢>jse?u{jk}luwe1glnlhÊosu�nlokc.osq.z|y{gle?g�cfo#oѵK�rluÏ�� jky~cie1zUokg�c.o?�

ü°ë ê�ë~ö°ë ®Éosbdh)u~±?osqÉosu`rlqdh)�lu~oszUeÃ©Ä å r ¢ okg�Åå r5u osg�Æ�Å}lb.e?glnlh�u{eUÄ1�h)qdz�}luwe|nlo�u~h)b�jky{gljkh�rl}lg�cfh)b�jkh)g\¯�r�ضr £�r3e1qfe�okuvnlh)z|y{gly~hlÅ�nlou{e�Á3�)}lq.e���u~h)b�±1e?u~h)q.okbpnlo|u�y{gAnly{jse?nlh)bpokg�oku{uweZ�

q q q qqq �q ��

��� �q �q

ºZyGb.o�y{gljkq.okzUokg�cfe?b.o�okuv±?e1u{h)q]nlo_u<okg³jse?n3e�}lglhÇnlo�u{h?b�rl}lg�cfh)b*nloku�jsh)g�c.h)q.glh�okg}lgle�z|y{u��osbdy{zUeA�ZnAokcfokq.z|y{g3e1qÈj`�h)z|h�b.o*z|hZnlyªÁ3j�e1q��� e�osu°±1e?u{h?qÈnlo*uwe�b.h?u{}ljky��h)g°�

¡)¡

Page 31: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ü°ë ê�ë~ü°ë ¬�h?glb.y~n��osqdosb.o*u{e�osjk}3e?jsy��h)g�nlo*»Âh?y{b.bdh)g�x Ä åârp|<osg�µ r�Ü ¢Hz�£TÞ]£�Ü ¢7z�£TÞjkh)géåN� Ç�È�r ¢A��Æxosz|h)bdc.qfe?q|��}lo�b.y�nly{bdjsq.o�cfy~Ã�e?z|h)b�jkh)g�û r � t g��}lz|osqdh"nlonlyª±Ky{b.y~h)glokb|okg�É\r g��}AzUokq.h´nlo<nlyª±Ky{b.y~h)glokb|okg��0v��\g�}lz|osqfe1zUh)b|u{h?b|gAhZnlh?bUnloy~Ãs��}ly{okq.n3e�e�nAosq.okji¦3e���nlo*e?qdq.y~�3e�e�e?�3e�·dh¶t jsh?zUh�e?u^osbdjsq.y~�ly{q�osg�u{h)b�q.osgA�)u{h)gAosbÈnlo}lg"js}3e?nAosq.gAh�v���okg�c.h)gljkosb�uwe�zUe1cfqdy{Ã|jsh)qdq.osbdr^h?glnly{okg�cfo�e?u:z\�okcfhKnlh�nlo�nlyªÄÅosqdosgljkywe?bÁ3gAy~cie1bpjsh)gÇuwe�Ä1�h)qdz�}lu{e�nlo*u{h)bpjky{gljkh|rA}lg�cfh)b5osb

x/û qJÊËËËÌw �� w �� w � � �� � � w

Í�ÎÎÎÏnlh?glnloe��osb8uwe�z�eMcfq.y~Ãpy{nlokg�cfy{nle?ndt�û�x'£v�£¶t�û x'£vG�_wÔosb:uwe�z�eMcfq.y~ÃÈcfqdy{nly{e?�)h)g3e1unlo*u{e?bpzUy~b.zUe?bÈnly~zUokglb.y~h)glokbpjsh)g��n����r�x5�|�¥�n� ¬ r £*r3e?q.e�� D�x¥Nu�*r £)�

ü°ë ê�ë¤�©ë �ÂhKn3e*ÄÅ}lgljsy��h)gwå�bd}AÁ3jsy~osg�cfokzUokg�cfo�q.ok�)}lu{e?q8��}lo]b.o�e1gK}Au{o�okg�uwe*ÄÅq.h)g�c.osqfenlokuOjs}3e?nAqfe?nlh�µ²r`Ü ¢HzÚ×#ÞN£�Ü ¢HzÚ×#ÞOb.o|rl}losnAo�osbdjsqdy{�ly~q�nlo|ÄÅh?q.zUe��}lgAy{j�e�jkh)zUh�}lglebdosq.y~o�ÄÅ}lgljsy~h)g3e?uPnlosu°c.y{r�hå1tL��z¡lvNr 0B�§Ð ¿ 2 � � � ¿ $ � ¿ t���z�lHv jkh)g $ � ¿ t���z�lv�r b.okg�t � × ¢ �]vAb.osg�t � × �âlHvÄ e�v�Æ�e?glnAh´r�h)q�bd}lrl}lokbdcfh"osbdc.o�q.osbd}lu~cfe?nlh'�Ênlokb.jsh?glb.y~nlosq.e?glnlh³rlq.h)�Au{oszUe?b�nlojkh)g�±)osqd�)osgAjsyweZ�Prlqdh)�3e?qÉ��}lo�u{e�okjs}3e1jsy��h?g Ä å·o « å¶r�¢A�IåN� Ç�È�r�¢A��cfy~osglo%b.h?u{}ljky��h)g�}lgAy{j�e�r3e1qfe « æ ¡ � q °{ñ���cfy~osglo*y~gAÁ3glyªcie?bÈbdh)u{}Ajsy{h?glosbÉr3e?q.e « r ¡ � q °{ñA��IvB¹�e?u~uwe?q©osuKz|osglh)q « r3e?qfe]osuK�K}AoÈosuKosbd�K}AoszUexnloÈnlyªÄÅosq.okgljsy{e?b©Á3gly~cfe?b Ä > � Â�� ¬ o« ÂÑ� ¬ r ¢�jkh)g)¯)r;Ø�rå£�cfosgA��eÇy~gAÁ3glyªcie?b�bdh)u{}Ajsy{h?glosb���jkh)zUrle?qfe?q�oku�q.okb.}luªcie?nlhjkh)g�oku`nlosu©e1r3e?qdcfe?nlh|e?g�cfokq.y~h)qs�ü°ë ê�ëÍ�°ë ¬�h)glbdy{n8�okq.osbdo�uwe�osjk}3e?jky��h)g�nlo�²©e?rlu{e?jso1� Ä åÛr�¢A��osg#okuBjk}3e?nlq.e?nlh]µÙrÜ ¢Hz�£TÞ1£PÜ ¢7z�£TÞvjkh)g�uwe1bxjsh)gAnly{jky{h)glokbxnlo�jkh)g�cfh)qdglh Ç�ÒÇ�Ó räx�£�bdy��\rÞ£)�`¢ æ l æ £)�åArÞ¢Çokg"oku:qdosbmcfh<nAoUu{e�ÄÅqdh)g�cfokqfe�nlolµ����]rlq.h�µZy{zUe?q�uwe�bdh)u{}ljky��h)g´}Ac.y{u{y~Ã�e?gAnlh�uweÄ1�h)qdz�}lu{e�nloxjky{gljkh�rl}lg�c.h)bpjsh)g¶¯¥r¿Øhr £°{×A�*b Ö1( Ô?t�®5okjs}8�okq.nlokb.o*��}lo�uwe%nlosqdy~±1e?n3eglh?q.zUe?u Ç�ÒÇ�Ó bdo*nlokÁ3gAo�jkh)zUhJÔ·å¥� í nlh?glnlo í osb5uwe�glh?q.zUe?u°o�µKc.osq.y~h)qp}lglyªcie?qdyweA�ü°ë ê�ëÍ�°ë ²©e|u~uwe?zUe?n3e�Õ ¼�3���]Ö,½ ¶ �#�G½}�ó º Öj�Z×3�H��Ö º ôn�ó ��u{e�Ä1�h)q.z�}Auwe�nlo%u{h)bÉjsy~gljshrl}Ag�c.h)bÉq.okb.r�h)glnlokg#e�uwe?bÈz|h)u��osjs}Auwe?bÈjkh)z|rl}Acie1jsy{h?g3e?u{okb

¡{×

Page 32: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

� Ø �Ø Ù �¹Ú Ø� Ø � �

�� ÙÛØ �

ºZose?g<Õ Ä�Ü � Ä � u{h)bph)r�osq.e?nlh)qdosbÉnly~b.jsqdokc.h)bÉjsh)qdq.osbdr^h?glnly{okg�cfosb]jsh)gd¯wr¿Ø^�e�vÈ»�q.h?�3e?qÉb.y~gÇz|y{q.e?qpe�uwe�c.osh)qs�� e���}lo Ä � å¥x Ä å�r¹ÆwtǯqÐvÈr3e1qfe0åÛ¦�� " �Á �Ivp»�q.h)�le?qÉ�K}Ao Ä_Ü å?x Ä å�r > ���q Ä t Ä å]v�oPÆ¥tǯ " vÈr3e?q.e0åÛ¦�� � �j�v:�]b.e?glnlh�oku�e?r3e?qmcie?nlh�e?g�cfokq.y{h?qs��nlosz|h)bmcfqfe1q���}lo Ä_Ü å3oPt « x « q¡¯qÄ°Z£¥¡4vyåwr ¢okb�}lg3e�e?rlq.h�µZy{zUe?jky��h)gÇnlo�h)qdnlosg<��nlo�u{eUokjs}3e?jky��h)g Ä å0o « åÛr�¢Z��a�bxnlokjsy~qs�P��}lobdyüå�±)okq.yªÁ3j�e Ä å0o « åâr ¢A�losg�c.h)gljsokb Ä_Ü å�o¿t « x « q ¯ q °K£¥¡4v�åwrÈÆ¥tǯ " v��ü°ë ê�ë � ë ²©eUokjs}3e?jky��h)g\x Ä ådr |�osg µ�rkÜ ¢7z�£TÞ�£aÜ ¢Hz�£TÞY��åN� Ç�È�r ¢A�3cfy~osglo*jkh)zUhbdh)u{}ljky��h)g\å1tL��z�lHvVrXtL�dxã�IqÄv6t�lhx�l7qÚv*jk}3e?glnlh�|~tL��z¡lv}rØ¡t��âoél¥xP�Iq/x�lnqÚvx�å1tL��z¡lv�r � � q�b.okg�t � �]vAbdosg�t � lv5js}3e?gAnlhd|~tL��z�lHver ¡�bdosg�t � �]vAb.okg�t � lHv��%aGµZrlu{y~j�e?qr�h)q���}8�o�okg�osuPrAq.y{z|osq8j�e?bdhl�3e?uPe?rlu~y{j�e1q8u{e�Ä1�h)q.z�}luwe%nlo�jsy~gljsh�rA}lg�cfh)bpjkh)gd¯¥rpØhr£°6û�oku�okq.qdh)q�jkh)zUo�cfy~nlhwtÅosu�z��eMµZy{z|h�nlo·� å1t�����z�l ¬ v xÝÂÑ� ¬ � v�osb8jsosqdhl�Oa�g�osu�b.ok�)}lglnAhjse?b.h|b.o�cfy~osglo�u{e�b.y{�?}ly{okg�c.oxcie?�Auwe�nlo%osqdq.h)qdosbstû à Õ ï î ña�q.qdh)q ×*m΢�ï1Õ}��£�¢ �n÷ ¡#m ×?��ï±�)£�¢ �n÷ £TmÎÕ{×4×±��£�¢ �n÷ £6m ×A£¥¡3��£�¢ �n÷ £Tm ¢)¢?�V��£�¢ �n÷

Æ�e?gAnlh�r^h)qpbd}lrl}lokbdc.h���}lo�aOqdq.h)q ¡ �ů4É)�3jse?u{jk}luwe1qÈosu`h)qdnlosgÇosz|r`�� q.y{jkhl�� ü°ë ê3ë� ºZo�e·ªeÜ å�Þ]r�Æ q � å�°§Æ�� q � o°Æ q � å]°,Æ�l q � �O»�q.h)�le?qÉ�K}Ao%rle?qfe0å�¦�� q � � qªeÜ åIÞ�tL����z�l ¬ v�r £¯ q � q �B¿ 2 � t�x%£v ¿ ì ¡#¢� ð � å1tL���Þ� �*� ¿ z�l ¬ vüo»å�t�����z�l ¬ � �#� ¿ v � oaÆwt�¯ q vÄ ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3t »�}loknlo�b.okq��}Zcfy{uOjkh)glb.y~nlosq.e?q�u{e�Ä1�h)q.z�}luweÇosu{okzUokg�cie?u±tÏ¡#b.okgl¦a��v q � r« q �¿ 2 � t�x%£v:¿<� q �¿ � újq�ß �*� ¿ � ­ ��b.}Ab]nlokq.yª±?e1n3e?bÉosg���r ¢A�Á ü°ë ê�ëÍ& ºZ}lr�h)gl��e?z|h)b°��}lo:b.o:e?rAu{y{jse�osu�zÊ�okc.hZnAh5nAo�nly~ÄÅokq.osgAjsywe1b°Á3gly~cfe?b©e?u�rlqdh)�lu~o��zUe¶x Ä å�r |�osg¥¯ r=Ü �Iz�¼ÚÞ�£aÜà@#z�ë�ÞBjkh)g�¯¶r Øwr�£°Tû³��nlo%z�e1glosq.eU��}lo�bl�h)u{h|b.o

¡1�

Page 33: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

n3e1g|jkh)glnly~jsy~h)glosb�okg�uwe?bGÄÅqdh)g�cfokqfe?bOb.}Ar^okq.y{h?qvoÉy{gAÄÅokq.y{h?qst�å1tL��z�@6vNr5u � tL�]vÑ��å�t���zÚënvNru q tL�]v�z|y{osg�c.qfe?b���}lo�osg�u~h)b�b.ok�)zUokg�cfh)b�±)okqdcfy~j�e?u~osb|b.o�e?rlu~y{j�e#u{e'Ä1�h?q.z�}lu{e#nloÇu{h)bjky{gljkh�rl}lg�cfh)b�nAokÁ3gly~osglnAh�Â~½�� � ¬ rá � ½ � ¬ �� � � ¬ ráÂ�½�½ � ¬ �%Æxosz|h)bdc.qfe?q]��}lo�osubdy{bdc.oszUe|u~y{glose?u`��}lo%b.o�h?�Acfy~osglo%osb]b.y{okzUrAq.o*jsh)z|r3e1c.y{�lu~o�nlokc.osqdzUy~g3e?nlhl���Âq.e1cie?qÉnlookgljsh)g�c.qfe?qp}lgle�jkh)gAÁ3�?}lqfe?jky��h)g��)okh)z\�okcfqdy{jse���}lo*q.osrAq.osbdosg�cfo%osbmcie?bÉy~nlosg�cfyªÁ3j�e1jsy{h?glosbnlo*u~h)bpglhKnlh)bs�ü°ë ê�ë ê�+`ë aGµArAu{y{jse?q�j`�h?zUh�b.o|rl}loknloUe?rlu{y~j�e?q�osu�z\�okcfhKnlh�nlo|nly~ÄÅokq.okgljsy{e?bxÁ3glyªcie?br3e1qfe�e?rlqdh�µZy~z�e?q�uwe�b.h?u{}ljky��h)g�nlo*uwe�okjs}3e1jsy��h?g�nlo*h)gAn3e?bÆ�qÚåÆ� q x Æ�qÚåÆ� q r ¢ �DÀ�¢Hz5¢ æ � æ £å1tL��zf¢�vNrp|~t��]vÄz Æ�åÆ� t���zi¢�v�r5u�t��]vå1tY¢7z¡��vNr¹å1tm£{z¡��vNr ¢ü°ë ê�ë ê�ê3ë ��osnly{e?g�cfo'uwe>qdos�)u{e>nlo�uwe>jse?nlokg3e¿tÅosz|rlu{ose?glnlh>Ä1�h?q.z�}lu{e?b�nlokuxcfy~r^hÇ�ÒÇ�â r Ç�ÒÇ � Ç �Ç�â o Ç�ÒÇ � Ç �Ç�â vÑ�ÂnAosz|h)bdc.qfe?q*��}lo|osg"jkhZh?q.nlokg3e?n3e?b%r�h)uwe?qdosb�oku:u{e?rlu{e?jsy{e?glh�b.ookb.jsqdy{��o*jsh)z|h Ä åâr Æ�qÚåÆ�� q o £� Æ�åÆ�� o £� q ÆIqÚåÆ�ã q  �Écfy{u~y{Ãse?q�okbdcie�o�µZrlqdosbdy��h)gÇ��}lg3e�nly{bdjsqdokcfy~Ã�e?jky��h)g�okg�u{e��K}Ao�u~h)bpy{gljkq.okzUokg�c.h)bÉnlo³���ã�bdo�e?g'£�� � °?ÕA�Zr3e?qfe�okb.jkq.y{�Ay{qÈ}lg�okb.��}loszUe�nlo�nlyªÄÅosq.okgljsy{e?b�Á3gAy~cie1bÈ��}lo*e?rlqdh�µZy~zUou{e\bdh)u{}Ajsy��h?g nAo³u{e\okjs}3e1jsy��h?g nlo³²©e?rlu{e?jso Ä å=r ¢A�±åN� Ç�äkr � � q oal q nlh)glnloÅãrå-7tL��z¡lv\tU£(ß��IqIoÛlnqòß�£�ÕHzN� æ ¢HzZllæ ¢ /��*b Ö1( Ô?tOºZo5h)�Acfy~osgloÉ}lgUb.y~bdcfokz�e��}lo*glh|b.o*rly~nlo*q.osbdh)u~±?osqk�:�]}lg�e?b��� oku`oзdosqdjsy~jsy{h�okb]u{e?q.�?hl�ü°ë ê�ë êKö°ë ¬�}le?glnlh�bdo�osz|rlu~o�eUokuGz\�okc.hZnlhUnlo�nAy~ÄÅosqdosgljkywe?b5Á3glyªcie?b5r3e?q.e�q.okb.h)uª±)osqu{eËosjk}3e?jky��h)g nloÊ»Âh?y{b.bdh)g okg�}lg nlh)z|y{gAy{h\js}lqm±)h5Å nlyªÄm�� jky{u�nlo´cfqfe1glbdÄÅh)qdz�e1q�okg}lgÔjk}3e?nlq.e?nlh\jsh)g }lgÔj�e1z��ly{hÊbdosgljky{u~u{hl�Éb.o�jkh)glbdy{nlokqfe?g u{h)blº � �!�ó��#� Õ ��� º ôn��� ¶h)�ZcfosgAy{nlh)b8r^h?q�uwe%y{g�cfokq.bdosjsjky��h)g�nloxuwe1b�q.okjkcfe?bȦlh)qdy{Ãkh)g�cie?u~osbO�U±?osqdc.y{jse?u{okb�nloxu{e�zUeM�u~uwe�jsh)g�ÆVÅx�<¬Èe?n3e�glhZnAh<y{g�c.osq.y~h)q*osbmcie?ql�e<q.hKnlo�e1nlh<r�h)q%h?cfqdh)b�jk}3e1c.q.h#glhKnlh)bk�Â�)ebdo�e?gÇy{g�cfokq.y~h)q.okbÈh�nlo�ÄÅq.h)g�cfokqfeA�O»�qdhZjkosnly~osglnlh�jkh)zUh�okg�u{e�Ä1�h)q.z�}luwe�nAo%jky{gljkh�rl}lgZ�c.h)bs�©b.o�rl}Aosnlo|osgljkh)g�cfq.e?q*}lg3e�jsh)z��ly{g3e1jsy��h?g�u{y{gAo�e?uÂnlo�u{h)bx±1e?u~h)q.okb�nlo�uwe�ÄÅ}lgljky��h)gokg�osu{u~h)b���}lo�e?rlq.h�µZy{z|o�okuvuwe1rluwe?jkywe?gAhl�]�]rlu{y~j�e?q5osbmcie�y{nAo�e�e?uBrlqdh)�lu{okz�e Ä å�r�¢A�åN� Ç�äJr�×*��xa� q xPl q nlh)glnAo�Å�r8-7t���z�lv tJ� q oél q ßÙ×*��zVlÝæ�¢ /��°c.h)zUe?glnlh¯wrÈØ?r&£)�

¡4à

Page 34: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÌÎÍ ü°ë ê3ë êZü°ë a�b.jkq.y{�Ay{q�}lg�rAq.h)�)q.e?zUe³�Ç���ɲ©�3á h³§BÓ}®Â��®5��­itÅu{h'rlq.y~zUokq.hokbxz+�e1b�b.okgljsy~u{u~h�vÈ�K}Ao�e?rlu~y{��}lo�okuÂzÊ�okc.hZnAh�nlo�nAy~ÄÅosqdosgljkywe?b5Á3glyªcie?b�e?uÂrAq.h)�lu~oszUeUnlojkh)g�cfh)qdglh�tÅ}lgly~nly{z|osglbdy{h)gle?u�vx/å m m o»åâr¿|Iz å1t��nv�rc@z å1t�¼6vNrÈëI 

�Bqfe1cfe?qpnlo*osbmcfy~z�e?q�osz|r`�� qdy{j�e1zUokg�c.oxjs}p�e?u`osb5osu`h)qdnlosgÇnlo*uwe�e1rlq.h�µZy{zUe?jsy��h)g°�ÌÎÍ ü`ë ê3ë ê��Bë a�bdjsq.y~�ly{qp}Ag<rlqdh)�)qfe1z�e������ɲ`�3á ��}lo�e?rlq.h�µZy{z|o�uwe�bdh)u{}ljky��h)g�nlou{e�osjk}3e?jky��h)gÊnlo�»Âh)y~b.b.h?géx Ä åérê|�osgvµ`riÜ ¢Hz�£TÞN£�Ü ¢Hzs£TÞ�jkh)g åN� Ç�È�r ¢�r3e?qfejk}3e?u{��}ly~osq3¯Ûr�ضr £°Tû´�±ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3t'a�g�}lglh�nlo�u{h)b]rlq.h?�lu{okz�e?b]e?g�cfokq.y~h)q.okb�b.onlokb.jkq.y{��o*o�µZrluÏ�� jsyªcie?z|osg�c.oxuwe�zUe1cfqdy{Ãxnloku`b.y~bdcfokz�e�qdosb.}Au~cie1g�c.o?�ÌÎÍ ü°ë ê3ëYên�°ë ®Éos¦le?jsokq�osuvrlqdh)�)q.e?z�e|nlosuGoзdosqdjsy~jsy{h�e1g�c.osqdy{h)q]r3e?qfe���}lo�r�osqdzUyªciejkh)glnly~jsy{h?glosbpnlo�ÄÅqdh)g�cfosq.e|�?osglokqfe?u~osbÉnlosu°c.y{r�h0åN� Ç�ÈÛr�u��^#Ü _ @sà.B à�ç�áOâUä`WÊç\C�áOâUä�©ë ê�ë ê3ë Æ�e?nlh\osu�rAq.h)�lu~oszUe�x/å�m m]o�å�r £)�/å1tY¢�v�r å1tУv�r ¢A¸%¦3e?u~uwe?qUuwe?be?rAq.h�µZy{zUe?jsy~h)glosb�nAo�u{e'bdh)u{}Ajsy��h?gË��}loÇb.o�h)�Acfy~osglokg�e1upy{z|r^h)gAosq�uwe'jsh?glnly{jky��h)g\nlo¾*e?u{okq�ç�y{g�jkh)gÇj�e?n3e�}lgAhUnlo*u~h)bpb.y~�)}ly{okg�cfosbÉjkh)gM·d}lg�cfh?b5nAo*ÄÅ}Agljsy~h)glosbÉ�3e1b.oe�v~è � rå- $ t��¥x�£�°{×�vÄz $ tL�hx�¡4°*×�v�/�jsh)g $ tL�]v�r zUeMµ�tY¢Hzs£°{×±xp� �N� v���Ivmè q r©-¥b.okg�t � �]vÐzfb.okg�tÏ¡ � �]vÐzfb.okg�t�× � �]v�/��j�vmè ÷ r©-��1tm£�xA�]vÐz¡� q tm£�x)�]v�/���©ë ê�ë~ö°ë ��rlu~y{jse?q�osupzÊ�okc.hZnAh´nAoÇoku{okzUokg�c.h)b�Á3glyªcfh)b|e x/å�m m�o¿åÈr �©�Zå1tY¢�v?rå�mLtУvZr ¢A�3jsh)gAb.y{nAosqfe1glnlh�u~h)bÉglhKnlh)b�� ¬ réNn°{×Z� N·r ¢7z�£4zÑ¡7z�×dt c��h)z|osbdo*osgd� � �â� qu{e�ÄÅ}lgljsy��h)g�cfoE·.e?nlh|¦3e?�lyªcf}3e?u���osg¶� ÷ bl�h)u{h�u{e�zUyªcie?n�y~Ãs��}ly{okq.n3e�nlo*oku{uwe4v���©ë ê�ë~ü°ë ®5okr^o�cfy~qGosuZrlq.h?�lu{okz�e]e?g�cfosqdy{h)qÂr^okq.h*e?¦Ah)qfe�jkh)g�uwe1bÂjkh)glnly~jsy{h?glosb~å1t ¢�vNr¢A��å m tm£vÅr £)�´¬�h?zUrlqdh)�3e?q�osg\e?z��^h)b�rlq.h?�lu{okz�e?b�js}É�e1gÊjsosqdj�e#okbdc��e#u{e<b.h?u{}ljky��h)ge?rAq.h�µZy{zUe?n3e�nlo*js}AzUrlu~y{qÈu{e�jsh)gAnly{jky��h)g�b.h?�lq.o}å�mLtУv���©ë ê�ë¤�©ë ¹�e1u{uwe1q�uwe�zUe1cfqdy{Ã�nloUqdy{�)y~nlosÃ���osuv±?osjkc.h)q%nlo�j�e?qd��e�js}3e?gAnlh�bdo|e?rlu{y~j�eokuÈz\�o�cfhKnlh�nlo�osu~osz|osg�cfh?b�Á3gly~c.h)b�e x/å�m mo�tL��o ¡4v�åérø£)��å�tyx�£�v?r`å1tm£�vhr ¢jkh)glb.y~nlosq.e?glnlh|u{h?bpglhZnAh)be� ¬ r�N7°?¡�jkh)glN·r�xx¡7zTx�£4zf¢Hz�£4zÑ¡K�8»Âe?qfe�b.y~zUrAu{y~Álj�e?q8u{h)bj°�e?u{jk}lu{h)b�osz|rlu��okosb.o*��}lo ý � $ q� r�x ý � $ q÷ rÈî ý � $ � $ q r x3î ý � $ q $ ÷ r�x �� �

¡?Õ

Page 35: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�©ë ê�ëÍ�°ë ¹�e1u{uwe1qÈuwe�ÄÅh)qdz�e��)okglosq.e?u©nlo*uwe�zUe1cfqdy{Ã�nlo%q.y~�)y{nlokÃ�jsh)qdq.okb.r�h)glnly~osg�cfo�e?urlqdh)�lu~oszUe±x/å�m mÍo}åwrp|B�#å1t ¢�vNrÈå�mLtУvNr ¢Ér3e?q.eeû glhKnlh)b`y~�)}3e?u~zUokg�cfovokb.r3e?jkywe?nAh)bs��©ë ê�ëÍ�°ë ºKo�e�osuÂrlq.h?�lu{okz�eÛxÅtL�Iå�m vymur�|Â��å1tУv�r�å1tÏ¡4vòr�¢Z�%ºZ}lr�h)gl��e?z|h)bx��}lookb.jsh?�)y{okglnlh�uwe?b8ÄÅ}lgljsy~h)glokbp�3e?b.o_- $ tL�]vÄz $ tL�·xË£°1��vÐz $ t��·x�£°?¡4v�/%jsh?gÇjky{okqdcie $ cfe?u��}lo*b.h?r $ rÙÜΣ4zÚ×4°)¡#ÞY�luwe�zUe1cfqdy{ÃxnAo%qdy{�)y~nlosÃ�okb

ÊÌ ¡{×4ñ�°M��î x�£�ï4°Z£¥¡ ¢x�£ï{°Z£¥¡ ñ�ï4°K£�Õ x3à4°{×¢ x3à4°{× ×?��×�°M��îÍÏ

¬Èe?u~js}lu{e?q�uwe�zUe1cfqdy{Ãpnlo5q.y~�)y{nAosÃpjs}le?glnlh�b.o5jsh)glbdy{nlokqfe?g|��}ly{gAjsoÉÄÅ}lgljsy~h)glokb8�3e1b.o?�  $ ¬ �h)�ZcfosgAy{n3e?b�e'r3e?qmcfy~q�nlo�uwe?b�e?g�c.osq.y~h)q.okb�nlo�uwe#ÄÅh)q.zUe#g3e1c.}lqfe1uÈjsh)g�¦lh)z|h?c.osjsy{e?b��c.qfe?bduwe?jky{h)glokbs��ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3tÇ»Oqdh)�3e?qprAq.y{z|osqdh���}lo  $ ¬ tL�]v�r $ tÅ�{�?x �Ì� � ¬" vÑ��©ë ê�ë � ë ¬�h?glb.y~n��osqdosglbdo�u{h?bBgAhZnlh?b¢(r¹�I� æ � � æ ����� æ � ½Pr&£8jkh)g}����� � x±���ur£°6û³��»�q.h?�3e?qp��}lo�uwe�z�e1c.q.y~Ã�jsh?q.q.okb.r�h)glnly~osg�cfo%e?u^osbd�K}AoszUe�nAo�nly~ÄÅokq.osgAjsywe1b�Á3glyªcie?br3e1qfe"oku�rlqdh)�lu{okz�eax/å�m m}r |Â��å�t ¢�v¶r å1tУvdr ¢A¸�jsh)y~gljsy~nlo<jkh)g�uwe´z�e1c.q.y~Ã�nloqdy{�)y~nlosÃÇe?uÉe?rAu{y{jse?q�osuÉz\�okcfhKnlh´nlo<oku{okzUokg�c.h)b�Á3gly~c.h)bdt b.e?u~±?h"z�}luªcfy~rlu{y~j�e?jky��h)g>r�h)q}lgle�jkh)glbmcie?g�cfojv���©ë ê�ëÍ °ë »�q.h?�3e?q���}lo�b.y�|>okb%jkh)glbmcie?g�cfo�okg´oku�rlq.h?�lu{okz�e�e1g�c.osqdy{h)qxokg�cfh)gljkosb%osuz\�okc.hZnlh5nlo:nly~ÄÅokq.okgljsy{e?bBÁlgly~cfe?bB�*okuZnAo8oku{osz|osg�c.h)bBÁlgly~c.h)bÂnle?g�okuK±1e?u~h)q`o�µAe?j�cfhxnlo8uwebdh)u{}ljky��h)g�osg�u{h)b8glhKnlh)bs�~b Ö1( Ô?t���}lgl��}lo�«ê�jë $ ë���uwe�b.h)u~}ljsy��h)gwå�jsh)y~gljsy~n3e?g�okg�u{h)bglhKnlh)b�r�h)qd�K}Aom� ërÈå1tL��ëÍv���okb�h)��±Ky{h*��}lopglh*u{h�¦3e1jsosg�okg|c.hZnlh?bvu{h)bGrl}lg�cfh)bOr�h)q.��}lou{e%rlqdy{z|osq.e*ÄÅ}lgAjsy��h?g�osb8u{y{gAo�e?u�e�c.q.h)Ãkh)b8�|u{e%bdos�)}lgAn3e�glh�u~h�okb}t r3e1qfe�| Ãì ¢�vÑ�Oa�bdcfoÄÅokgÉ�h)z|osglh�osbmc��e�q.okuwe?jky{h)g3e1nlh�jsh)gÇuwe�u~uwe?zUe?n3e ó?Ö?����� ¾ � º ×Z���Rí!� ºO¾ õ ¶Z��©ë ê�ëÍ&°ë ºZose?gÇuwe?bÈÄÅ}lgAjsy{h?glosbÉjs}le?nlq3�eMcfy{jse?bÉe�cfq.h?Ãsh)b$ � r86 �*�1tm£�xA�]v b.y©¢0ß���ß&£

¢ osgÇh?cfqdh|jse?b.h $ q r îïð ïñ�1tY¡#�wx�£v bdy©¢hß��Ûß�£tY¡#�wx ×4vTtL�¥x\¡4v bdy�£.ß��Ûß ¡¢ okg�h?c.q.h�j�e1b.h

�]rlu{y~j�e?qÈoku`z\�o�cfhKnlh�nlo*osu~osz|osg�cfh)bÈÁlgly~c.h)bÉjsh)gÇuwe?bÈÄÅ}Agljsy~h)glosbÉ�3e1b.o $ � t��]v�� $ q tL�]v��$ � tL�0x�£vÑ�le?u^rlq.h)�Au{oszUe?xeå�m mo)åwr��Iq~x"¡#�0x³¡Z�7å1tY¢�vNrÈå1tY¡4vNr ¢��Ujsh)z|rlqdh)�3e?q��}lo]uwe*b.h)u~}ljsy��h)g�h)�Acfokgly{nle�jsh?y{gljky{nloÉjsh?g�uwe*o�µAe?j�cieA�ZÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3t�»Âe?qfe%b.y{z|rlu~y~Á3jse?qu~h)b�j°�e?u{jk}lu{h)b�osb�jkh)g�±)osgAy{osg�c.o�glh1cie?q��K}Ao $ q osb�bdy{z\�okcfqdy{jse�r�h)qÅ��r £)�´�5c.y{uÏ�� jsokb.ocfe?z��ly��osg���}loÅý $ q � r ¡�ý $ qq rÈîZý $ � $ q r �� � �¡4ï

Page 36: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÌÎÍ �Bë ê3ë ê�+©ë ®5okrlq.okb.osg�cfe?q��)ql�e1Á3jse?zUokg�cfoÉuwe?b�ÄÅ}lgAjsy{h?glosbOh)�Ac.osgly~n3e?b:osg|j�e?nle%}lgAhnloÉu~h)b�e?r3e1qdcie1nlh)bOnlosu3rAq.y{z|osqGrlq.h)�Au{oszUe���jkh)zUrle?qfe?qGosu3q.okb.}luªcie?nAh%jkh)g�uwe�b.h?u{}ljky��h)goѵle1jkcie(åâr £1x�jsh)bd¦e�eo�¸�bdosgl¦���jkh)gw¸Jr�tÅjsh)bd¦*£�x'£v¡°vbdosgl¦*£3r ¢*mÎ�)Õ�¡Z£)£ïK£Z T j ÌÎÍ �©ë ê�ë ê�ê3ë a�uwe1�^h)q.e?q*}lg>rlqdh)�)q.e?z�e������ɲ`�±á���}lo�e?rlu~y{��}lo|osu:z\�o�cfhKnlh<nlooku{osz|osg�c.h)b�Á3glyªcfh)b�e<u{h?b�rlqdh)�lu{okz�e1b�nlo�jkh)g�cfh)qdglh�nlo�u{e�ÄÅh)qdz�e\x/å�m mHo¿¸�åãrg|Â�å1t��nvNrÈå1t�¼6vNr ¢A�A��nly~�l}M·do�u{e��?q3�e1Á3jse�jsh)qdq.osbdr^h?glnly{okg�cfo?��©ë~ö`ë ê3ë ¹]e?u{u{e?q:}lg3e�ÄÅ}lgljky��h)gâå�¦��(qt�Ü ¢7z�£°)¡#Þ v8jkh)gâå1tY¢�vNrÈå1tУ°)¡4v~r ¢�cie?u°��}lor3e1qfe�cfhKn3e_ò�jkh)g�okbdcfe?b]z|y{bdz�e1b�j�e1qfe?j�cfosqs�� bmcfy{jse?bÉb.o*js}AzUrlu{e

����q� tLå m ò m o¿t �{å?x�£v:ò7vNr ¢H �©ë~ö`ë~ö°ë aObdjsqdy{�ly~q]okuGrlqdh)�lu{okz�e�x��Iå m m xaå m o�¡*åÛr £?�]å1tm£�vòr å m t�×�vòr ¢|osg�bd}ÄÅh)qdz�}lu{e?jsy��h)g�n��os�ly~u`�<e1rlu{y~j�e?qdu{o�osuBz\�okcfhKnlhUnlo�oku{osz|osg�c.h)b]Á3gAy~cfh?b]okzUrlu~o�e?gAnlh�bl�h)u{hnlh?bÉÄÅ}Agljsy~h)glosbÉ�3e1b.o?t nlo�c.y{r�h´«mcfoE·.e?nlh)¯l�Auwe�b.ok�)}lgln3e�nlyª±Zy~nly{nle�r^h)qpu{e�zUyªcie?n�v���©ë~ö`ë~ü°ë ºZo*jkh)glb.y~nlosq.e|oku`rlq.h?�lu{okz�e�okg�Õ �Z�R� ¶ ��õ�×Z���Rí!� ºO¾ õ ¶�osg�§ ÷x5nly~±üt O t��]v�Ô·å�vNr¿| osg Åcó�§ ÷

nlh?glnlo O osb�}lg3e�z�e1c.q.y~Ã�nlokÁ3gAy{n3e�r�h)bdy~cfyª±1ea×\£�×A�åa�b.jkq.y{�Ay{q�b.} ÄÅh?q.z�}lu{e?jsy��h)gn8�ok�ly{uP�3e¥·dh|uwe?bpjkh)glnly~jsy{h?glosbpnlo%Æxy~q.y{ji¦Au{okc���nlo%­]ok}lz�e1glg°�DÎÄÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3tǬÈe?u~js}lu{e?qrlqdy{z|osqdh�nly~±ut}ò O t��]v�Ô·å�vÑ��©ë~ö`ë¤�©ë Æ�e?nlhÇosu:rlq.h)�Au{oszUe�nlo�jkh)g�cfh)qdglhÛå m m rå¡Z�1å1tУv.r;å1tyx�£v(rØ¢A�Âjs}A�)ebdh)u{}ljky��h)g�okb3å1tL�]vZr¿�IqDxÔ£)¸�osbdjsqdy{�ly~q5bd}�ÄÅh)qdz�}lu{e?jsy��h)g�±1e?q.y{e?jsy~h)g3e?uP��jkh)gljku{}ly~q5��}lor3e1qfe�cfhKn3e0åÛ¦��}q5jsh)g¶å1tm£vNr�å�tyx�£�vZr ¢�b.o%js}lz|rlu{o

î × o �� � � t�å m v q o��4å]v~æÔ¢H � �©ë~ö°ë�� �Âq.e1cie1qvnloÉnlosz|h)bmcfqfe1q�uwexnlokb.y{�?}3e?u{nle?n|e?g�cfosqdy{h)qGnly{qdosjkcfe?z|osg�cfo1��b.y{g�okz��rlu~o�e?qpu{e�ÄÅh)q.z�}luwe?jky��h)gU±?e1q.ywe1jsy{h?g3e?uÏ�Kb3�h?u{h�jsh?g<e?qd�)}lz|osg�cfh?b5nAo%j°�e?u{jk}lu{h�oku{okzUokg�cfe?uÏ�

¡{î

Page 37: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�©ë~ö`ëÍ�°ë ºZo�e<oku�rlqdh)�lu~oszUe\x/� tL�]v�å m m o¹¼*t��]v�å m oc@*tL�]vyåarê|�nlh)glnlo¥�#��@�b.h?gÄÅ}lgAjsy{h?glosbvokbdc.q.y{j�cie?z|osg�c.opr^h)bdy~c.y~±1e?bs�BÆxokzUh)bmcfq.e?qG��}loÉz�}luªcfy~rlu{y~j�e?glnAh5r�h)qv}Ag3e�ÄÅ}lgZ�jky��h)gÇe?nlokjs}3e1n3eUbdo�rl}Aosnlo�osb.jkq.y~�ly{qÉosgÇuwe�ÄÅh)qdz�ewxÅtd �]tL�]vyåIm vym{o  @*tL�]vyå�r  |���¦le?u{u{e?qbd}ÇÄÅh)qdz�}lu{e?jsy��h)g�n8�ok�ly{u`�3e�·dh|u{e?bpjsh?glnly{jky{h)gAosbòå1t��nv�r¹å1t�¼Äv�r ¢Z��©ë~ö`ë � ë ¬�h)gAb.y{n8�osq.okb.o%uwe�osjk}3e?jky��h)g��ly{e?q.z��h)gly~j�e�okg�Å�ó�§ qÆ " åÆ�� " o�¡ Æ " åÆ� q Æ�l q o Æ " åÆ�l " rp|

�3e�·dh|u{e?bpjsh?glnly{jky{h)gAosbòåâr Ç�ÒÇ�Ó r ¢�osg�Æ�Åx�:Æxosz|h)bdc.qfe?qp��}lo*b.}�ÄÅh)qdz�}luwe1jsy��h?g�n8�os�Ay{uokb ä Ä å Ä ò0r ä |Oòr3e1qfe�ò'okgÊjsy{okqdc.h<osbdr3e?jky{h#nlo|ÄÅ}lgljky{h)glokb�t okg>q.ose?u{y~n3e?n³osgdôÛq� tLÅ�v¡v*bfe1c.y{bmÄ e?jsy~osglnlhu{e?bpzUy~b.zUe?bÈjkh)glnly~jsy{h?glosbpnlo�ÄÅqdh)g�cfosq.eA�ZÎÄÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3t�¬Èe?u~js}lu{e?qÈrlqdy{z|osqdh Ä t Ä å�vÑ�

�©ë~ö`ëÍ °ë »Âe?qfe·¢dr�£4zÑ¡nzÚ×Hzj j T Èb.ose?g�u{e?bÈÄÅ}lgljky{h)gAosb| � tL�]v�r 6 ¢ � bdyu��¦»Ü x �q � z �q � Þ�q b.�)gütL�]v bdyu��¦»Ü x�£{z�£TÞ�x¹Ü x �q � z �q � Þ

ÆxokzUh)bmcfq.e?qÈ��}loÅ| � c.y{osgAo%nAosq.yª±1e?n3e�n8�os�Ay{u°��}lo%osbmc��e�}lgly~ÄÅh?q.z|osz|osg�cfoxokgÛªÂ���l����}lor3e1qfe�js}3e1u{��}ly{okqÈÄÅ}lgljky��h)g]uw¦��¥t�ܤx%£4z�£TÞ v�b.o%js}AzUrlu~ou{y~z� ­ 0 �� � | m� u·r�uut ¢�vÄ 

Æxoknl}ljsy~q���}lo�glh�o�µZy{bmcfo�gly~gl�)}lg3e%ÄÅ}lgljsy��h)g�nlo±ª � ��}lo�bdo�e�osu^uÒ�� zUyªcfo.t okg�ª � vOnlo}| m� �õ �nô ¶ZtÉ­5h�h)�lbmcie?g�c.o?�Pu{e|c.osh)qs�� eUnAo�nly~bdcfqdy{�l}Ajsy{h?glosb]n3e�}lg#bdosg�cfy~nlh�e�okbdc.o�uÒ�� zUyªcfox�bdo%nAy{jso*��}lo.| m� jkh)g�±)okq.�)o�e�uwe�nly{bmcfqdy{�l}ljky��h)g�nAosu~cfe�nlo%Æxy{qfe1j?�ÌÎÍ �©ë{ö°ëÍ&°ë ºZok�È�}lg*}lg%rlq.h)�Au{oszUeÉe?g�cfokq.y{h?qs�¥uwe?b°ÄÅ}Agljsy~h)glosb©jkh)g.å1tyx�£vNr�å1tm£vNr ¢nlok�^okg'bfe1c.y{bdÄ e1jsosq � ÷ o¹ý �� � � t�å�m vyqZo��4å]v³æ�¢A��a�b.jkq.y{�Ay{qx}lg'rlqdh)�)q.e?zÚ§BÓV®G��®É�x­��}loÉn3e?nle*}Ag3exÄÅ}lgljsy��h)g�öݦ�� q jkh)z|rlq.}lok�^o5e?rAq.h�µZy{zUe?n3e?z|osg�cfo�osbdcfe%nAosb.y~�)}3e?u~n3e?nr3e1qfe�åpr tL� q x £voö�tL�]vÑ� �Écfy~uÒ�� jkosbdoÇu{e³qdos�)u{e´nlo#ºZy{z|rlbdh)g�r3e1qfe"e1rlq.h�µZy{zUe?q�uwey~g�c.os�)q.e?uP��oku`jshKjsy~osg�cfo*y{gAjsq.okzUokg�cie?u°rle?qfe�e?rlqdh�µAy~z�e1qÈuwe�nlokq.y~±1e?nleA�

¡{ñ

Page 38: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÌÎÍ �©ë~ö°ë ên+`ë ºZy�b.o´cfh)zUe å=r « ½�32 � � � jsh?bt�÷ q tÏ¡*¢�o £�vy�]v�osg osu*rlq.h?�lu{okz�ee?g�c.osq.y~h)qs��osg�c.h)gljsokb*uweUnAosb.y~�)}3e?u~n3e?n#y~g�cfos�?qfe?u©b.o�c.qfe?gAbdÄÅh)qdz�e|osg�}lg3e�nAosb.y~�)}3e?u~n3e?n��}loÈy~g�±)h)u~}ljsq.e�u{h)b�� � �GaObdjsqdy{�ly~qG}lg�rlqdh)�)q.e?z�e]§BÓ}®Â��®5��­���}loÈ�l}lbd��}lopr3e?q.exj�e?n3eû u{h)be� � tÅnly{�)e?zUh?bpjsh)g�� � ¦�Ü x3×4°)¡7zÚ×�°?¡#Þ�vÈr3e1qfeUu~h)b5�K}Ao�uwe�o�µZrlqdosbdy��h)g#h?�Acfokgly{n3eokb5z��� gAy{zUeA�GÆxy~�l}M·.e?q8uwe��)ql�e1Á3jse�nAo�uwe�ÄÅ}lgljky��h)gâå�q.okb.}luªcie?g�cfox��jsh)z|rlq.h?�3e?qÈ��}lo*b.or3e1q.osjko%e|u{e�nloV�IqDx�£)��©ë~ü`ë ê3ë ºZose?g $ � z $ q z $ ÷ uwe?b`ÄÅ}lgljky{h)gAosbG�le?b.o3t rly~q3�e?z|y{nAo�v°e?bdhZjkywe?n3e1bÂe5u{h)bBglhKnlh)bnlo*jky{osqmcfh�cfqdy��e?gA�)}lu{h�ø nlokzUh)bmcfq.e?qp��}lo $ � o $ q o $ ÷ ì £%okg ø>��©ë~ü`ë~ö°ë ��rlu~y{jse?q©osuAzÊ�okc.hZnAh�nloÈoku{okzUokg�c.h)bÂÁlgly~c.h)bveÅx Ä åNo·å�r £�okg�osuZjs}3e?nAqfeM�nlh�� �N�ÄoÝ� l��4ß�£%jkh)g�jsh)gAnly{jky{h)glokbpnlo*Æxy{qdy{ji¦lu~okc�¦lh)z|h)�Â�osgAo�e?bpokg�oku°uwe?nAh�b.}lr�osqdy{h)qnlokq.okji¦lhU��jkh)glnly~jsy~h)glosbpnAo�­5os}lzUe?glg�¦lh?zUh)�Â�osglose?bÉosgÇu{h)bph?c.q.h)bk�O�5c.y{uÏ�� jsokglb.o�bl�h)u{hnlh?bÉc.q.y��e?gl�)}lu~h)bstÂosu`jkh)q.qdosb.r�h)glnAy{osg�c.o�e�� æ ¢���oku`jsh)qdq.osbdr^h?glnly{okg�cfo�e0�ÛßÔ¢A��©ë~ü`ë~ü°ë �Écfy{u~y{Ãse?qGoku�zÊ�okc.hZnAh%nAo]oku{osz|osg�c.h)b�Á3gly~c.h)bOosglµ rÙÜ ¢HzÑ¡#Þn£�Ü ¢HzÑ¡#Þ�jkh)g|u{h)bjk}3e1cfqdhÇc.q.y��e?gl�)}lu~h)b�nlo�cfosqdzUy~g3e?nlh?b%r�h)q*uwe1b*e?q.y~bdcie1b%nAolµÞ�'oku:rA}lg�cfh tУ4z�£vÑ�©r3e?qfee?rAq.h�µZy{zUe?qÈuwe�bdh)u{}Ajsy��h?gÇnAosu`rlqdh)�lu{okz�ex Ä å�r ¢Hz å1tY¢Hz�lHv~rÈå1t���zi¢�vNr ¢7z Æ�åÆ� tY¡7z�lHv~r ¢Hz Æ�åÆ�l tL��zÑ¡{vZr&£4 

ÎÐÏ Ñ{ÒÇÓ¡ÔnÓÄÒ�ÕÖ Ï3t���rlqdh¥±?osji¦3e1q%oku¦Aosji¦lh�nlo���}lo�b3�h)u~h�nlh)b�nlo�uwe1b5ÄÅ}lgAjsy{h?glosbx�le?b.o�rle?qm�c.y{jsy~r3e?g�qdo�e?u~zUokg�c.o�osgÇosu`rlqdh)�lu~oszUeA��©ë~ü`ë¤�©ë ®5okr^o�cfy{q`oku�rlq.h?�lu{okz�epe?g�c.osq.y~h)q©e?¦lh?qfep�3e¥·dhÉuwe1b`jsh)glnAy{jsy~h)glokbüå�t ¢Hz�lHv~r¹l��Ç�ÒÇ � tL��zÑ¡{vNr ¢A�å1tL��zf¢�vNr ¢A�å1tY¡7z�lHv~r ¢A��©ë~ü`ëÍ�°ë ºZoseUu{e�ÄÅ}lgljsy��h)gÇnlokÁ3gAy{n3e�r^h?q $ tL��z¡lvNr�tУex���b.�)g�t��]v¡v6tm£�x l�b.�?g�t�lHv¡vokgaµ rÙÜ x�£4zs£TÞ]£Jܤx%£4z�£TÞ^��r�h)q8jsosqdh�osg�h?c.q.h�jse?b.hA�:¬�h)g�osu~uwe�bdo�rl}loknlosg�jsh?glb.y~nlo��q.e?qÉosu{okzUokg�cfh)b5Á3gly~c.h)bÉjs}3e1nlqfe?gA�)}luwe1q.osb5osg<u{}l��e1q5nAo%c.q.ywe1gl�)}lu{e?q.okbs�È�]rlq.h�µZy{zUe?qÉuwebdh)u{}ljky��h)g�nlo(x Ä åeoÛåâr¹�Il^� Ç�ÒÇ �xùù Ç�ä r ¢Z�Kjkh)ggÅãr�Ü ¢Hz�£TÞ7£¶Ü ¢7z�£TÞY�K}Zcfy{u~y{Ãse?glnlh�jkh)zUhÄÅ}lgAjsy{h?glosb5�3e?bdo�u{e?bÉq.osbmcfqdy{jsjky{h)gAosb5elÅ nlo $ tL��z�lHv�� $ tL�¥x�£4z�lHv�� $ tL�wx�£{z�l�x�£v��$ tL��z�l.x+£v���©ë~ü`ëÍ�°ë ¬�h)gAb.y{n8�osq.okb.o%uwe � ¾ Ö ¶¢¾ õ#¼� º �#��½ ¾�¶ ½��Z�Æ�åÆ� x Æ�qÐåÆ� q r¿| z å1tY¢7z¡��v~rÈå1tm£{z¡��vNr ¢Hz å�t���zi¢�vNr�uut��]vÄ 

×)¢

Page 39: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

»Âe?qfe\e?rlu~y{jse?q�oku�z\�o�cfhKnlhÊnlo�osu~osz|osg�cfh?b�Á3gly~c.h)b�eÊosbmcfo�cfy~r^h>nAo´rAq.h)�lu~oszUe?bs�5b.oy~zUr�h)gloÈu{exjsh)gAnly{jky��h)g�nlo]¾*e?u{okq�ç�y{g�jkh)g·å�t���z¡��v�r « �jëÇt���v $ ëÇt��]vÂ� $ ëZuwe?bvÄÅ}Agljsy~h)glosbc.oз.e?nlh|¦3e?�Ay~cf}le?u{okbs�Èa�b]nlosjky{qs��bdo�bd}lr^h?glo���}lo%u{h)bÉjkhZo�Á3jsy~osg�cfokbM�jë`nlosr�osgAnlosg#nAo(�Ñ�ÆxokzUh)bmcfq.e?qÈ��}lo%osbdc.hUu~u{o�±?e�e�}lgle|okjs}3e?jky��h)g�nlyªÄÅosqdosgljkywe?u°nAo%u{e�ÄÅh)q.zUeO � \� m tL��vüo O q \��tL��vNr \¼ jsh)g � ¬ tY¢�vNr�uut�� ¬ v

nlh?glnlo O � � O q b.h?g�z�eMcfq.y~jsokbs��¬Èe1u{js}Auwe?qduwe?b�jk}3e?glnlh�b.o5cfh)zUe?g�uwe?bOÄÅ}lgljky{h)gAosb:�3e?b.oe?bdhZjkywe?nle?bÉe�uwe�nly~b.jsqdokc.y{Ã�e1jsy��h?g�� ¬ r°Nn°{×�jsh)gJN0r ¢7z�£4zÑ¡7z�×A�ÌÎÍ �Bë~ü°ë � ë aOu{e?��h)qfe?qB}lg�rlqdh)�)q.e?z�e]�����ɲ`�±áÊ��}loÈr�osqdzUyªcie5e?rlu~y{j�e1qÂokuAz\�okcfhKnlhnloÇosu~osz|osg�cfh?bUÁ3glyªcfh)bUePx Ä ådoÝåpri|Â� Ç�ÒÇ ��ùù Ç�È rø¢A�Èokg�µ r Ü ¢HzÚû�Þs£ÈÜ ¢7zÚû¶Þ}Ac.y{u~y{Ã�e1glnlhpjsh?zUh5osu~osz|osg�cfh)bBuwepr3e1qdcfy~jsy��h)g*osg�jk}3e?nlq.e?nlh)bB}lgly~n3e?n*�*jsh)z|h5ÄÅ}Agljsy~h)glosb�3e1b.oÇu{h)b�c.qfe?bduwe?n3e1nlh)b�nlo�uwe#ÄÅ}lgljky��h)g $ t���z�lHv?r tm£.x¹� b.�?g�tL�]v�vTtm£Åx¹l�b.�?g�t�lHv¡vqdosbdc.q.y~gl�)y{nle�eµ rÙܤx%£4z�£TÞü£»Ü¤x%£4z�£TÞY�l��}lo�e?r3e?qdosj?�� e�osgÇ}lgÇrlq.h?�lu{okz�e�e?g�cfokq.y~h)qs�ÌÎÍ �©ë~ü°ë� °ë �ÇhZnlyªÁ3j�e1q�osu�rlq.h)�?qfe?zUe<nlo�oku{osz|osg�c.h)b�Á3glyªcfh)b�r3e?qfe#��}loÇe?nAzUyªciejkh)glnly~jsy{h?glosbÉnlo�Æxy{qdy{ji¦lu~okcpglhU¦lh)z|h)�Â�okglo�e?bp��jkh)zUrAq.h)�3e1qpgK}Az\�okq.y{jse?z|osg�cfo1��bd}lbdc.yª�c.}A�)okglnlh�nlyªÄÅosq.okg�cfosb]ÄÅ}lgljsy~h)glokbxosg#u{e|ÄÅqdh)g�cfosq.eA�PokuGrlqdy{gljky{rly~hUnAosuBz+�eMµZy~zUh|r3e?q.e�uweokjs}3e?jky��h)g\x Ä å¶r ¢A�~õ �nô ¶Kt8a�gÇosbmcfo%rlq.h)�Au{oszUe���osg�osu`bdy{�)}ly~osg�cfo*bdo�bd}lr^h?glo���}lobdo*c.y{okglo*osu`rlqdh)�)qfe1z�e�nlo*oku{osz|osg�c.h)bÈÁ3glyªcfh)bp��}lo%b.o*r�osn`�� e�okg�u{e�rlq3�e?j�cfy~j�eA�ÌÎÍ �Bë~ü°ëÍ&°ë ��hKnly~Álj�e?q]osuGrAq.h)�)q.e?zUeUr3e?q.e���}lo�e?nlz|y~cfeUjkh)glnly~jsy{h?glosb]nlo·®5h?�ly{gnlo�u{e�ÄÅh?q.zUewåwoé¸ Ç�ÒÇ � rÿ¢A�U¬�h)z|rlq.h)�le?q*gK}Az\�okq.y{jse?z|osg�cfo���}lo|js}3e1glnlh�¸+jkq.okjso?�u{e³b.h?u{}ljky��h)g+bdo#r3e?qdosjko'e"uwe"h?�Acfokgly{n3e³�3e¥·dhÊuwe1b�jsh?glnly{jky{h)gAosb�nAo�­]ok}lz�e1glg�¦lh1�z|h)�Â�okglo�e?bk��©ë¤�Bë ê3ë ¬�h)glbdy{n8�okq.okb.o|osuvokb.r3e?jky{h�ú r8-*|ã¦P�¥t�Ü ¢7z � Þ vÞt»|~tY¢4v3r=|~t � v/r ¢j/jkh)g>osuOrlqdhZnA}ljkc.h#osbdj�e?u{e?q�}Ab.}3e?u3t nAowªNqÄv��B�³bdo�e¥ûåosu:b.}l��osbdr3e?jky{h#�)okglosq.e?nlh#r�h)q-¥bdosgò��zfb.okg�tÏ¡#�]vÐzfb.okg�t�×*�]v�/��:¹�e?u~uwe?q8uwe�nly~bdcie1gljsy{e�nAo³u�t��]vNr¹�1t � xA�]vÈeJû|��©ë¤�Bë~ö°ë ºZo�eüµ�ý � Ð ½�þ r -*|�¦��?t¡Ü ¢HzÚû�Þ�v tg|~tY¢4vwri|~t�û�vâr ¢Hzw| ùù ý ¬ Ð ¬ � � þ rÄÅ}lgAjsy��h?gÇjk}3e?nlql�e1cfy~j�eA�Ar3e?qfe�c.hZnlh|¢¥ß�N æ ûÝ/��pÆxokzUh)bmcfq.e?qÉ�K}Ao�µ ý � Ð ½[þPosbdc3�eU�)okglo��q.e?nlh�r^h?qÈcfqfe1b.uwe1jsy{h?glosbpokg�c.osq.e?b]nAo%u{e?bÈÄÅ}lgljky{h)gAosb

$ � r 6 �*�1tm£�xA�]v b.y©¢0ß���ß&£¢ osgÇh?cfqdh|jse?b.h $ q r îïð ïñ

�1tY¡#�wx�£v bdy©¢hß��Ûß�£tY¡#�wx ×4vTtL�¥x\¡4v bdy�£.ß��Ûß ¡¢ okg�h?c.q.h�j�e1b.h

×A£

Page 40: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�©ë¤�Bë~ü°ë �Écfy{u~y{Ãse?glnlhÉosuKq.okb.}luªcie?nAh�e?g�c.osq.y~h)qBnlosz|h)bdc.qfe?qB��}lo�u{e5bdh)u{}Ajsy��h?g�nloexeå m m ot���o £vyåér � ÷ o¹�IqÂo¹��x ¡Z�Nå�m�tY¢�v0r�¢A��åIm tm£�¢�v0rÚ¡?¢#jkh)y{gAjsy{nAo�o�µAe?j�cie?z|osg�cfojkh)g"u{eÇh)�ZcfosgAy{n3e�r^h?q%oku8zÊ�okc.hZnAh�nlo|osu~osz|osg�cfh?b%Á3gAy~cfh?b¥tÅjsh)g³uwe?b*ÄÅ}lgljky{h)gAosb%�3e?b.oy~glnly{jse?n3e?b�v��

×�¡

Page 41: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÿ ââ@�æ�UVCsâ�ç�à*ä

Page 42: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...
Page 43: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

Û|ÜØÝ ßàxáOâ�ã³âUäåã³à æ´ç è´é�ä�âê3ë ê�ë ê3ë »Âe?qfe�q.okb.h)uª±)osqÉu{e�osjs}le?jsy��h)g°�3�3e?bmcie�b.okr3e?qfe1q5u{e?b�±1e?qdywe?�lu~osb

l m o»l q r ¢�� x l�ml q r�£�� £l r¹��o £¡ � l·r £�0o £°)¡  

²©eÉb.h)u~}ljsy��h)g#«mo�µZrlu{h1cie?¯5osg(��r�x%£°)¡Z�­]h]b.o:jsh)g�c.qfe?nly~jso:osu�cfokh)q.okz�eÉnlo8o�µZy{bmcfosgAjsywer�h)q.��}lo��osbmcfo:b3�h)u~h�e1b.os�?}lqfe?�le]uwepoѵAy~bdc.osgljkywe]nAo8bdh)u{}ljky��h)g*okg�}lg�osg�cfh)qdglh0tÅnloOcie?zUe� glhy~glnlokc.osqdzUy~g3e?nlh�v:nlo*uwe�jsh?glnly{jky��h)g�y~gly{jkywe?uY�ê3ë ê�ë~ö°ë e�v�ºZy�bdoUjk}lz|rlu{y~osqfe)�è� � �N�{x+¢]�uß®øã� �¶x+¢ � �©nly~±Ky~nly{okglnlh�osg�c.q.oJ� �N�3�c.h)z�e1glnlh�uÏ�� zUyªcfokb�js}le?glnlh·��¾ ¢A�lb.o�c.osglnlqs�� e�}lg3e�jsh?g�c.qfe?nAy{jsjky��h)gP��IvȲ©e�z+�e1bph)��±Zy{e�osb�l � ì ¢A��®Éosbdh)u~±Ky{okglnlh�uwe�okjs}3e1jsy��h?gÇnAo%u{e�ÄÅh)q.zUe�¦3e1�ly~c.}3e?utÅb.}lr�h)gly~osglnlh|r�h)qpoзdokzUrlu~h·lwÀ�¢�vÑ�3b.o�cfy~osglo*��}lo(lut��]vZrÙtL�?xvøJv�qÄ°1��osb5b.h?u{}ljky��h)gnloÅlnm]r � l�������qxokg��AÀ�ø>¸`u~h���}lo�r�osqdzUyªcfo*Ä e?�lqdy{j�e1q�g�}lok±1e?b�b.h)u~}ljsy~h)glosb�r^ok��e?glnlh}lg�cfqdh)Ãsh�nlo}l � �:»Âh)qpoE·dosz|rlu{hl q t��]v�r86 ¢ b.yu�ÛßÔ¢� q °1� b.yu��æÔ¢ l ÷ tL�]v�rá6 ¢ b.yu��ß�£�°)¡t��¥x�£�°)¡4v q °1� b.yu� æ�£�°)¡

� jjv�Óx��±Zy{e?z|osg�cfo�u~hU��}lo�¦le��Ç��}lo�rlqdh)�3e?q]osb]�K}Ao�uweÔ�}Agly{jseUb.h?u{}ljky��h)gÛ�(q�okbxuwey~n��osg�cfy~j�e?z|osg�c.o�gK}AuweA�ºZ}lrp�h)gl��e?bdo8��}lo:o�µZy~bdcfo:}lg3eÉb.h?u{}ljky��h)g.�(qBnloZlnm7r�� l�������q��#l�tY¢�vNr ¢5jkh)g.l�t��nv±Ãr ¢r3e1qfe�e?u~�È�}lgd�d¦�tyx�£4zs£v5jkh)g�l�t��nv3À ¢�tÅosuBh?cfqdh�j�e1b.h�osbxe?gÉ�e?u~h)�)h��<bdo�zUokgljsy~h)g3ez��e?bÉe?nlokuwe?g�c.o�v��Oa�gÇ}lgÇosg�cfh)qdglh|nlo O ��l�glh�bdo�e1gK}Auwe���b.o*cfy~osglol m r=� l�� ����q � l m l ����q r £�� l�tL�]vNrÙt��wxvøJv q °1�z ��Àéø� »Bh)q�jsh)gAbdcfqd}ljsjky��h)gP�8u{e<b.h)u~}ljsy��h)gÊglh'g�}luwe��}q��l}lbdj�e?n3e'nlok�^o�jkh)y{gljky{nly~q�jkh)gÈtL��xøJvyqа1�|r3e?qfe0�JÀ5ø tÅgÉ�h?c.osb.o���}lo�z|y{okg�cfqfe1belâÀÔ¢�b.o%cfy~osglo*}lgly~jsy~n3e?nIvÑ�ȺZyÑø æ ¢bdo]u~u{os�)e�e%}lgle%jkh)g�cfqfe1nly{jkjsy��h?g|jkh)g¥l�tY¢4v~r ¢A�OºKy�øùÀ+¢*glokjsosb.e?q.y{e?z|osg�cfoel�osb:g�}luweokg³oku:y~g�cfosqm±1e?u{h�Ü ¢Hz�øÛÞ�r�h)q*b.okq�jkq.osjky{okg�c.o?�1lnmxæÿ¢���jk}lzUrAu{y{qVl�tY¢4v3r=l�tLøJvVr ¢A�r�osqdh|okg�cfh)gljkosb/lnm m7r ¢�okg<oku`y{g�cfokq.y{h?qÈnlo*nly{ji¦Ah|y~g�cfosqm±1e?u{h�z|y{osg�c.qfe?bp��}lo}l�m mHr�£°)¡bdyu��À�ø>�lokb]nAosjsy~qs�l�æ�� q �a�g"nlo�Á3glyªc.±1eA�©osu��}lgly~jsh�j�e?bdh<r�h)b.y~�lu{o�okb<ø r ¢Z��ºZy�bdoUjk}lzUrAu{y{okqfeâl�tL�]vVr ¢r3e1qfed� æ ¢A��r�h)q�bdo�jsqdosjsy~osg�cfo�bdo�u{u~os��e?qs�� e�nlo�g�}lok±?h´e#�K}Ao�u{y{z ��­ ��� lnm mDr ¢�Ãru~y{z ��­ ��� lnm mZr £�°)¡Z��¬�h?gÊ}lg\e?q.�?}lzUokg�cfh#bdy{z\�okcfqdy{jkh<e?u8nlosu8rÉ�e?qdqfe1ÄÅh<e?g�cfosqdy{h)qk�vb.oc.y{osgAo���}loxbdy]l�t ¤ �nv æ ¢�rle?qfe�e?u{���}lg ¤ � æ ¢Z�Zokg�c.h)gljkosbòl�jsh)y~gljsy~nlo�jkh)g�xÅtL�Åx ¤øJv�qа1�

×�à

Page 44: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

r3e1qfes� æ ¤øÿ�%e?nlokz+�e?b ¤ø`r ¢A�Âa�bdcfh]u{u~ok±1eÈuwepuwepjkh)g�cfqfe1nly{jkjsy��h?g*Álg3e?u�u{y~z ��­ ��� l m m rx%£°)¡âÃr u~y{z ��­ ��� l m m r&£°)¡Z�ê3ë ê�ë~ü°ë áÈe1bdcie�osu~os�)y~qÈuwe�zUe1c.q.y{Ã

O r ÊËËËËËËËÌ¢ £ ¢ ¢  j j  ¢¢ ¢ £ ¢  j j  ¢¢ ¢ ¢ £  j j  ¢��� ��� ��� ��� � � � ���¢ ¢ ¢ ¢  j j  £x/��� x/� � x/� q x3� ÷  j j  x3� �#� �

Í ÎÎÎÎÎÎÎÏê3ë ê�ë¤�©ë ¹]e����K}Ao�rlqdh)�3e?q

b.}lr� ¬2��� X O l.x O ¤l�XXÐl.x ¤l�X r z�e¥µ � «�¬  ¬�u{e?qfe?z|osg�c.o�osu`rlqdy{z|osqÈz|y{okz��lq.h�bdo*rl}losnAo�okb.jsqdy{�ly~qpjsh)z|h

b.}Ar� ¬2 �X O \��XX \�xX r b.}Ar Ò 2 � X O \å�Xòr bd}lr Ò 2 � ç \å ­ O ­ O \åü 

Æxy{e?�)h)g3e1u{y{Ãse?glnlh O/­�O okg�}lgle|�3e1b.o*h)qdc.h)glh)qdz�e1uÏ�Kb.o�cfy~osglo*��}lo*o�µZy{bmcfo%}lg3e�zUe1cfqdy{Ãh)qmcfh)�?h)g3e?u[Â&��}lg3e�zUe1cfqdy{Ãxnly{e?�)h)gle?uNtÅglhUgAos��e1c.y~±1e�r�h)qpb.okq.u{h O ­ O v�cie?u~osbp��}lob.}lr� ¬2 �

X O \�xXX \�xX r b.}lr Ò 2 � ç \å ­  ­ ¨� \åâr b.}Ar�� � � Ò 2 � ç \ò ­ ¨ \ò� a�z|rlu{ose?glnlh���}lo]X? � � \ò�X�r®X \ò[X¥�Zr^h?qpb.osqGÂ�h)qdc.h)�)h)g3e1uÏ�Kb.o�h)�Ac.y{okgloxÄ1�e?jsy~u{z|osg�cfo]osuqdosb.}Au~cie1nlh�nlosbdo�e?nlhA�

ê3ë~ö`ë ê3ë �]u©e?rlu{y~j�e?q8osu`z\�okc.hZnlh�nlo%a�}lu~osqɦ3e�����}lo*y~c.osqfe1ql � � � r¹l � x»¯l q� jsh?gdl*�sr&£4 

²`h���}lo�u~u{o�±?e�el � r ×

� z l q r ×?�Õ?� z l ÷ r î1��Õ4×

£�Õ{×4î?� z l " r ¢ m �)��ñ4î{×)Õò j j ×)Õ

Page 45: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

²©eÉb.h)u~}ljsy��h)g�oѵAe?jkcfe]osb1lut��]vNr�£°Htm£�o.�]vÑ�?jkh)g�u~h5jk}3e?u�osuKosqdq.h)q©okbGosg%±1e?u{h)q©e1�lb.h)u~}Acfh¢ m ¢�à?¢A£�Õ4×ò j j ]¬�h)g#okuBc.osh)qdoszUeUjsh?q.q.okb.r�h)glnly~osg�cfo�b.o�h)�Zcfy{okglo�bdy{g�osz��3e1q.�)hUuweUjkh?cietÅb.o*¦3e�cfh)zUe?nlh·ª r ¡.rÔb.}lr·�ªÆ |u°§ÆIl���osg���¦ Ü ¢Hzs£TÞ�v�¡{ª t�ú� ß þ � ÿ �ux�£v¡¯?r ¡

¡±�¥¡ t�ú q�ßÍ� � � �ux�£v�� £� r ¢ m ï{ñ{î)Õ4×ò j j ²`h�js}3e1u`osbÉ}lg3e?b*£�Õ�±)okjsokb]zUe��)h)qÉ��}lo*osu`okq.q.h?q5qdo�e?uY�

ê3ë~ö`ë~ö°ë Ó���±Kywe1zUokg�c.oÈjsh?g�±?osqd�)o5exjsosqdh%e?uAoku{os�?y{q�l{�Âr ¢A��ºKyAb.opoku{y~�)oÂl*�sr&£�¢ � � � �r�h)q�oku8cfokh)q.okz�e#nAo�jsh)g�±)okq.�)okgljsy{eA�:osu�zÊ�okc.hZnAh#nlo�a�}lu{okq�nlok�^o�jkh)g�±)osqd�)osq�okg�}Agokg�c.h)q.gAhUnlo*u{e�jsh)glnAy{jsy��h)g�y{gly~jsy{e?uÏ�Ke�uwe��}lgly~j�e�b.h?u{}ljky��h)g�jkh)q.qdosb.r�h)glnAy{osg�c.o�nlo6 l�m7rk� l�������ql�tY¢�v~r�£�¢ � � �

a�bÉnlosjky{qk��e·l�tL�]vNrÙtL��o�¡±��£�¢ � � vyqа1�l�ê3ë~ö`ë~ü°ë e�vÈÆxy~q.okjkcie1zUokg�c.o?�lbdo�h?�Acfy~osglo�r�h)qposu`zÊ�okc.hZnAh|nAo�a�}lu~osql � � � r�tУDoP¸~¯Ivyl � oP¯º jkh)g l*�sr ¢7 

®Òc.osqfe1glnlh|b.o*u{u~os��e�el � r � tУÂoa¸~¯I¯Ivy�#� � oÈtm£DoP¸�¯I¯ vÌ�*� q o¹������o £ � ¯º�z��}lo1�3b.}lzUe?glnlh|uwe�rAq.h)�)qdosbdy��h)g��)okh)z\�o�cfqdy{j�e�okbs��r3e?q.e·¸éÃr ¢A�

l � r º¸ �ÄtУDoP¸~¯IvÌ�Vx+£ �  ºZy�¸Jr ¢|bdo*h)�Acfy~osglo�Ä1�e?jky{u~zUokg�c.o±l � r¹¢ü¯ºO��IvOÆxy~±Ky{nAy{osgAnlh%e?z���h)bOzUy~osz��lqdh)b�osg�c.q.o3lDoÛº1°{¸�o5y{g�cfok�)qfe?gAnlhl��b.o5u{u~os��e*e���}lou{e�±)osqdn3e?nlokqfe|b.h)u~}ljsy��h)g�osb lut��]vNr º¸ t�ú?� � x�£vÄ Æxoku`e?r3e?qmcie?nAhUe1g�c.osqdy{h)q

l4½Ar º¸ �ÐtУÂoa¸�¼Ä°TûÛv ½ x�£ � z ¯wrÙt�¼Âx\¢�v¡°6ûdz��}lo�cfh?z�e?gAnlh�uÒ�� z|y~c.osbÂûg¾ jsh)y~gljsy~nlo�jsh)g¶l�t�¼Äv��

×�ï

Page 46: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

Á j�vɺZo*nlokz�}lokbdcfq.eU��}lo ª r u{y~z½ ­ 0 � l�t�¼Äv�xAl4½V� ûokb�}lgle�jsh?glbdcfe?g�cfo�gAh�g�}lu{eA�Âbdo�nloknl}ljky{q3�e�u{hÇrlqdy{z|osq.h�tÅq.osjk}8�osqdnlosbdo?�Z¯Arä¼6°6û�v��©�cfe?z��ly��osg�u{h�bdos�)}lgAnlhl�3r�h)q.��}lo%osgÇosbdo%jse?b.hu~y{z> ­ �

� l�t�¼Äv1x l{½}�¯ É r u{y~z½ ­ 0� l�t�¼Äv�xAl4½V� û ɼ É r¹¼j� É ª�u{y~z½ ­ 0 û É � � r�¿ 

»Âe?qfe5j�e?u~js}lu{e?q`q3�e?rAy{n3e?z|osg�c.oDª#u~hÉzUoE·dh)q©osbG}Abfe?qB��}lo±tУ�o�¸1¼6°6û�v ½ r¹ú ½ À �nÁ�ßÍ� � � þ � ½ �·d}lg�c.hËjkh)g u{e?bÇe?rlq.h�µZy{zUe?jky{h)glokb�nlo"�Âe��Ku{h)q�u{h?�Itm£.o��]vAr �Axp�IqÄ°)¡?o�ÆwtL� ÷ v��ú � r�£Do»�0oPÆ¥tL� q vÑ�ljs}3e1glnlh·��¾ ¢Z�:¬�h)g�okbdc.hª r´u~y{zÝ� ú?� þ x�tУÂoa¸�¼Ä°TûÛv ½ � ûêr u{y~zÝ� ú?� þ x ú?� þ �ú*�j� � þ � �Rß q ½ �u�jú�� ß ½ � � �Ð� ûr u~y{z ùù ú?� þ x ú?� þ � £�x ¸1qмÚq¡*û oPÆ¥t�ûJ� q v � ùù ûgr ¸�qÚ¼Úq

¡ ú?� þ Ãr ¢H ê3ë~ö`ë¤�©ë ²©e�y~c.osqfe1jsy��h?g�osb]e?¦lh)q.e

l � � � rÈl � o㯠O l � r�t��3o㯠O v�l � jsh?gdl*�sr ì ££�ð  a�bdc.hUjkh)glnl}Ajso�e

l � r ì £Do�¡4¯ ¡4¯¢ £DoË¡4¯ ð � ì ££ ð rÙtm£DoË¡4¯Ivy� ì £ ¡4¯I°tУZo�¡4¯Iv¢ £ ð � ì ££ ð  §��e1jsy{u~zUokg�cfoxnlo%e?��}°�� bdo*nlosnl}Ajso

l �� r�tУÂoË¡4¯Ivy�Htm£Do ¡{¯�¢£ÂoË¡4¯ vÄz l q� r�tУZo�¡4¯Ivy�7 

²©epb.ok�)}lgln3e5osjk}3e?jsy��h)g%nlosu�osg�}lgAjsywe1nlh]y~zUrAu{y{jseÂlnqÂrÈújq � �1z|y{okg�cfqfe1bB��}loObd}lbdc.y~cf}Z�)osgK�nlh*okgUu{e*rAq.y{z|osq.eA�)z|osnly{e?g�cfopu{e?bvcZ�okjsgly~j�e?bO¦3e?�Ay~cf}le?u{okb�b.oÉu{u~os��exe}l��NrÈújq � tm£]o<¡�]v��ºZy�¯wr¹¼Ä°Tû³�3bdo�bdy{�)}lo���}lo(l �½ ¾ l � t�¼ÄvÑ��l q½ ¾ l q t�¼ÄvÈjs}3e?gAnlh?¢d¾ �a�upzUy~b.z|h�e?qd�)}lz|osg�cfh'nlokuprlq.h)�Au{oszUe'e?g�cfokq.y{h?q�rlq.}Aos�3e'��}loa� l7qjt�¼ÄvòxÈlnq½ �3ÃrÆ¥tǯ4Év�r3e?q.e Ê À £?�]okg r3e1qdcfy~js}lu{e?q�XÐl�t�¼Äv/xÝl{½³X¿Ãr Æwt�¯4Év��ÿ»Bh)q�h?cfq.e>r3e?qdc.o?�XÐl�t�¼Äv1x l{½³Xsr¿Æwt�¯Iv8osb5jsh)gAb.osjk}losgAjsywe|nlosu°c.osh)qdoszUe�nlo*jsh)g�±)okq.�)okgljsy{eA�×4î

Page 47: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ê3ë~ö`ëÍ�°ë �&r3e?qmcfy~qÈnlo}l � � � r¹l � oP¯�tУDo»� q� vpbdo*h)�Acfy~osglo*e1u`y~cfokqfe?q�jsh)g¶l{�Âr ¢A�l4½Ar(¯�tУÂo�¢ q vüoP¯�tУDo㯠q vüo¹�����joã¯�tm£Do¿t�û x�£v q vr}ûÛ¯�oã¯÷ tY¡{û x+£v× t�û x+£v�û¡

²©eÉb.h)u~}ljsy��h)g�oѵAe?jkcfe�osgżvosb�l�t�¼ÄvNr¿¼o�¼ ÷ °{×A�Mb.y~g�okz��3e?qd�)h�u{epb.h)u~}ljsy��h)g�e1rlq.h�µZy{zUe?n3ejkh)g�¯?r¿¼Ä°Tû osb l4½ r¿¼~oP¼Ú÷j� £× x £¡{û o £

Õ4û q �  ¬�h)gÇu{h�jk}3e?uül�t�¼Äv�xAl{½ÝÃrÈÆwt�û � qÐvÑ�ê3ë~ö`ëÍ�°ë »�q.hKjsoknly{okglnlh|jsh)z|h�osgÇosu`rlqdh)�lu~oszUe�e?g�cfosqdy{h)qk�ljsh?gd¼�r&£)�l4½»r}¯ q tY¢eoÔ£Âo�������oaû²x�£�v�x»¯÷#tm£DoË¢ q oÔ£ q o¹�����oÈt�û x�£v q vr}¯ q ûAt�û x�£v

¡ x»¯÷ tÏ¡{û x�£�v× t�û x�£�v�û¡r £¡ x £

¡{û x � £× x £¡{û x £

Õ4û q � r £Õ x £

Õ{û q¬�h)z|hÛl�tm£�vÅr £°?ÕA�vbdo�nloknl}ljsoA� lutУvDxél{½V��rg¯qа?ÕZ�'ºZy:osu�j°�e?u{jk}lu{h<e?g�cfokq.y{h?q�b.o¦3e1jso<jkh)gé¼Jr ¡K��cfh)zUe?glnAh ¯pr ¡{°Tû³�Èbdo#u{u~os��e�nlo�uwe´zUy~b.zUe�ÄÅh?q.zUe³e)l{½²rl�tm£v�o�¡4°TûkoaÆwt�û � qÐvÑ�lr^h?qpjsh)glbdy{�)}Ay{osg�c.o%gAh|bdo�jk}lz|rlu{ow� lutУv�x l{½}�*r¿Æ¥tǯqÚvÑ�

ê3ë~ö`ë � ë e�vpºZoseh���ur £�¢,Dd��¢?ß5D�ßpàK�3jsh)gÇu{h�js}le?u`uwe?bÉy~glnly{jse?jsy~h)glokbposbdcfe?q3�e1g�okgE���r�à?¢(x ����okb.r3e1jsywe1n3e?b�}Ag3e�nly~bdcie1gljsy{e¥¯drÿ£�¢Z�]�]uÂy~q]nlo�Ej��e]E � �Pu{e�±?osu~hZjky{n3e?nokbGEj�Ârpà?¢A�Z��osu°c.y{osz|r�h��K}Ao%bdo%cfe?q.nle�okbl � r�l{�1o ¯à?¢VxA�I� jkh)g�l{�Âr ¢H 

Æxoxu{e�zUy~b.zUe�ÄÅh)qdz�eA�Ze?u°y~q�nlo�E � e�E q �luwe�±?osu~hZjky{n3e?n�okbME � r¿à1¢3x�� � ��okuPcfy~osz|r^hc.qfe?glbdjs}lqdq.y~nlh�osb l q rÈl � o ¯à?¢±xA� �  ��e1b��� bd}ljsokb.yª±?e1zUokg�c.o?�:»Âh?qÈcie?g�cfh�oku^c.y{osz|r�h�cfh?cfe?uÏ��l � �losbpokuPqdosb.}Au~cie1nlh�nlo�e?rAu{y{jse?qoku�z\�o�cfhKnlh�nAoUa�}lu~osq�eâl m r声tÇà1¢Åxã�]v���l�tY¢�v±r ¢A�Bjsh)g)¯Ar�£�¢A�U�]u�¦3e?jkosq%uwe?bjk}losg�cie1b]bdo%h?�Acfy~osglol � r ¢eo £�¢à1¢ o £�¢

��¢ o £�¢×?¢ o £�¢¡?¢ o £�¢

£�¢ r ¡1¦�£�ï1zUy~g] ×4ñ

Page 48: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�Iv©a�bdcfh]b.okq��� eÉjsh?zUh]e?rlu~y{j�e1q`osu�z\�o�cfhKnlh5nlo�a�}lu~osq©js}le?glnlh±¯w¾ ¢A�Mjsh?g�u{hÉjk}3e?u�osuc.y{osz|r�h]okg�ÄÅ}lgljsy��h)g�nlokuAokb.r3e?jky{h�qdosjsh?q.q.y~nlh3l0rÈlut��]v©±?osglnlqs�� e�nle?nlh�r�h)qÂu{e�b.h?u{}ljky��h)goѵle1jkcie|nlo�u{e�osjs}le?jsy��h)g<nlyªÄÅosqdosgljkywe?u©e?g�c.osq.y~h)qs� �aObmcie|osb3l�tL�]vZr�x#u{h?�Itm£ex �]°4à?¢�v��bdo%jkh)z|rlq.}lok�3e��K}Ao%u~y{z ��­ � ��� lut��]vZrÈo³ �OaObÉnlokjsy~qs�3glh|u{u~os��e�g�}lgAj�eA�ê3ë~ö`ëÍ °ë a�bOz�}A��b.okgljsy~u{u{h�h?�Acfokglosq�l � r�tm£ o¶¯Iv � �nå � r�tm£ o¶¯I°)¡4v�q � ��»Bh)q�cie?g�cfhc.hZnlh�u~h��K}Ao�¦3e�����}lo*rlqdh)�3e?qÉokb

tm£Doã¯Ivy� æ tm£Doã¯I°)¡{v q � æ úT� >  aGµKcfq.e��?osglnAh�qfeA�� jsokb�¢�x��osb.y~z�e1b

£Doã¯ æ £Doã¯I°)¡ æ ú >  ²©e�rAq.y{z|osq.e�nlokb.y~�)}3e?u~n3e?n�okb�h)��±Kywe%�Uu{e�bdy{�)}ly~osg�cfo]osb8jsh)glbdosjk}losgljkywe�nloku^nlokbfe?qdq.h)u~u{hú > r £Doã¯.o㯠q °)¡�o¿t cZ�osqdzUy~glh)bÈr�h)bdy~cfyª±)h)b¡v��

� ê3ë~ö°ë�& ®Òcfosq.e?glnlh|uwe�Ä1�h?q.z�}lu{e�nlosu`zÊ�okc.hZnAh�nlo%aO}Au{osqÉbdo%h?�Acfy~osglol{½»r(¯�� £ç £ o £� £�x+£°Tû o £� £exÊ¡4°Tû o¹�����jo £� £�x�t�û²x�£�v¡°Tûr(¯ ç ûko㯠ç û � £ç ¡ o £ç × o������o £ç û �

²©e�y{gAnly{jse?jsy��h)g#b.o�bdy{�)}Ao�nly{qdosj�cie?z|osg�cfo�nAosuGc.osh)qdoszUe�nlosuG±1e?u~h)q�z|osnAy{h�e?rAu{y{jse?nlh�e|~t��]v0r £° ç �{��osgÈÜ ¢�z�¢do £TÞ8��Ü ¢�x�£{z�¢]ÞY�³�]u�}Ac.y{u~y{Ã�e1q.uwe�osg\oku�cZ�okq.z|y{glh#okg�cfq.or3e1qK�osg�c.osb.y~bÉb.o%u{u{ok��e�et ç ×Vx ç ¡4vüo¿t ç �}x ç ×{vüo¹�����oÈt ç ûkoÔ£�x ç û�v æ l{½)x»¯ ç û

¡4¯ ç û æt ç ¡±x ç £vüoÈt ç ×Vx ç ¡4vüo¹�����jo¿t ç û x ç û x�£vРºZy~zUrAu{y~Álj�e?glnAh�uwe?bpbd}lzUe?bÈcfoku{osbdj`�h)rAy{j�e1bÉ��h)r^okqfe?gAnlh

¡4¯ ç û q oPû x�¡4¯ ç ¡*û æ l4½)xa¯ ç û æ ¡4¯�û²x�¡{¯ ç û� ºZ}Abdcfyªcf}A�?osglnAhwûêr�£°{¯Ç��b.}Az�e?gAnlh?¯�����qZx�¡�e�c.hZnAh)bpu{h)bÈcZ�osqdzUy~glh)b

¡ ç £DoP¯hx�¡±x�tÏ¡ ç ¡±x�£vRô ����q æ l4½)x�¡ æ x3¯ ����q  ��¢

Page 49: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

¬�h)z|h�¡ ç £Doã¯wxË¡?r�Æwt�¯ vÑ�Pbdo�cfy~osglo��K}Ao�� l4½Ax�¡ � °4¯ É ¾ js}3e1glnlh Ê À�£°)¡tÅgÉ�h?cfokb.oU�K}Ao¥l�tm£vVr ý �� ë4�]° ç £�xA�arØ¡{v���a�bdc.h<glh�jsh)g�cfq.e?nly~jso|�K}Ao�osu:z\�okcfhKnlhnlo³a�}lu{okq�b.o�e�nlo"h?q.nlokg £)�x�)eË��}lo´uweÊÄÅ}lgljky��h)g¿|~tL��z¡lv\r £°�ç £exA� glhËokbdc3�eglypbdy{��}ly~osqfe��ly~osg�nlokÁlgly{n3e'osg�}lgËosg�cfh)qdglh´nloâ�pr £)�8jsh)g�u{h'jk}3e?upglh´b.o�cfy~osglobd}AÁ3jsy~osg�cfo%q.ok�)}lu{e?q.y~n3e?n�r3e1qfe���}lo�bdo*rl}losnleUe?rAu{y{jse?qÈoku°cfosh?q.oszUe�nlo*jsh?g�±?osqd�)osgljkyweA�ÌÎÍ ê3ë{ö°ë ê�+`ë tÏÓxz|y~cfy~nlh�vÑ�ÌÎÍ ê3ë{ö°ë ê�ê3ë tÏÓxz|y~cfy~nlh�vÑ�ê3ë~ü`ë ê3ë �5g3eUe1rlu{y~j�e?jky��h)g�nAy{q.okjkcfe�nAo%u{e�nlokÁlgly{jky��h)g�u{u~ok±1e�e

l � � � r¹l � o㯠t���l � oP¼Äv�o¿t���l � � � oa¼6v¡  �]u`nlosbdr^oE·.e?qÉb.o*h)�Ac.y{osgAo%u{e�Ä1�h)q.z�}luwe�nlo*qdosjs}Aq.q.okgljsy{e

l � � � r £Âoa�n¯ °?¡£�x �n¯ °?¡ l � o ¼Ä¯

£�x �n¯ °?¡ z jkh)g�l{�Âr ¢H ®Òc.osqfe1glnlh|b.o*b.y~�)}lo

l � r ¼Ä¯£�x»�n¯ °?¡ ì`£Do � £DoP�n¯I°)¡£�x �n¯I°)¡.� � o¹�����oPoa� £Doa�7¯I°)¡£ex»�n¯I°)¡.� �#� � ð  

ºZ}Az�e?gAnlh�uwe�rlqdh)�)q.okb.y��h)g��)osh)zÊ�okc.q.y~j�el � r ¼� ì � £Âoa�n¯ °?¡£�x»�7¯I°)¡ � � x�£ ð  

ê3ë~ü`ë~ö°ë �]u©e?rlu{y~j�e?q8uwe�Ä1�h)qdz�}luwel � � � rÈl � oã¯�t�l � � � oal � v�� l � � � r £DoP¯

£òxa¯ l �  ¬�}3e1glnlhhl{�Âr ¢��¶¯wr £�°Tû³�lbdo*h)�Acfy~osglo

l4½»r � £Do £�°Tû£�x�£°6û � ½ z��nlo%uwe�jkh)glhKjsy{nle�Ä1�h)qdz�}lu{e�£°tm£�xA�]vDr�£so �·oa�Iq~oPÆwt�� ÷ vpb.o%nlosnl}Ajso�øç l4½ar£Do�¡{°Tûko�¡4°6û q oPÆ¥t�û �n÷ v�b.y{z|rlu~osz|osg�cfo�r�h)qp�Âe��Ku~h)qs���]b��� rl}lokbøç l{½»rÈú qy� ½ tУÂoaÆwt�ûJ�n÷Ðv�v

�l£

Page 50: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

��uwe�Ä1�h)qdz�}luwe8nlo�uweÈy~glnly{jse?jsy��h)gxy~zUrlu~y{jseDl4½»r¹ú q tm£oVÆ¥t�û � q v¡v��¥hÉos��}lyª±1e?u{okg�c.osz|osg�cfo� lutУv�x l{½}�*r¿Æ¥tǯ q vÑ�l��e���}lo.l�tm£�v~r¿ú q �¶¯wr�£�°Tû³�²©e%nAosb.y~�)}3e?u~n3e?n�nlo5uwexy~glnly~j�e?jky��h)g�okb8jkh)glb.okjs}lokgljsy{e�nloÉ��}lo/ú ­ x?�Hx#£]cfosgA��e%}Agz��� gly~zUh*okgw��r ¢A�vÆxo�e?��}`�� tУ~oJ��v ½ x\£}ß�ú ½ ­ x\£���e?u^b.}lbmcfy~c.}ly{qZ�Or^h?qòÆwt�û �n÷ vbdo%h?�Acfy~osglo?tm£ZoaÆwt�û �n÷ v�v ½ x+£3rÈÆ¥t�û � qÚv��ê3ë~ü`ë~ü°ë a�uArlqdh)�lu~oszUeel�m7rp|~t���z�lv`b.o�rl}losnAoÈosbdjsq.y~�ly{qBosg�okuZy~g�cfosqm±1e?u{h�Ü � � z¡� � � � ÞÏ�y~g�c.os�)q.e?glnlhA�ljsh)z|h

l�tL� � � � v�r¹l�tL� � vüo � � � �� � |�tL�Ðz�l�tL��v�v�ë4�Р�]u©e?rlu{y~j�e?q8uwe�q.ok�)uwe�nAo%jk}3e?nlq.e1cf}Aqfe�nlosu°c.qfe?r�osjky{h�b.o*h)�Ac.osglnAq��� elut�� � � � v ¡ l�tL� � vüo � � � � xA� �¡ �y|~tL� � z�l�tL� � v¡vüoP|~tL� � � � z�l�tL� � � � v¡v ���u~h��}lgly{jkh���}lo�qdosbmcie�osbÉosbdjsq.y~�ly{qòl � ¡ lut�� � v���l � � � ¡ lut�� � � � vÑ�

ê3ë~ü`ë¤�©ë ²©e<qdos�)u{e�nlo�ºZy{z|rlb.h?g>y{g�±)h?u{}ljkqfe?qs�� e�l � owl � � � r3e?q.e<¦3e?u~uwe?q}l � � q �G�)e��}lo*b.o%�3e?b.e�osgÇuwe�Ä1�h)q.z�}luwe�nlo*jk}3e?nlq.e1cf}lq.e � � � �� � u ¡ � � � q x)� �Õ � u�tL� � vüo��,u�tL� � � � vüovu�t�� � � q v �  

­5h|bdosqs�� e�}lgÇz\�o�cfhKnlh�nlo*}lg�rle?b.h|b.y~glh�nlo*nlh)bs�� ê3ë~ü°ë�� aOgÇj�e1n3e�r3e?b.hl � � � rÈl � o ¯

¡ �Ì|~t�� � vüoP|~tL� � � � v � zz|y{okg�c.qfe?bp��}lo*u{e�bdh)u{}Ajsy��h?g�q.o�e1u`bfe1c.y{bdÄ e1jso

lut�� � � � v�r�lut�� � vüo � � � �� � |~tL��v�ë4�Р®Éosbmcie?glnAh�e?z��3e?bposjk}3e?jky{h)glokblut�� � � � v�x l � � � rÈl�tL� � v�x l � o�¯ �jkh)g ¯ � r � � � �� � |wx ¯ ¡ �Ì|~tL� � vüoã|�tL� � � � v �  

��¡

Page 51: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ºZ}Az�e?gAnlh�cfhKn3e?b�okbdcie1bUy~�)}3e?u~n3e?nlokb�r3e?q.e�¢Ýr ¢Hz�£{zj j j ÄzÚûíx�£?�:bdo�cfy{okglo���}lo�osuokq.q.h?q�osbdc3�e³e1jsh?cfe?nlh'r^h?qh¯5b.}Ar·� ¯ � � �:b.y{okzUrAq.o���}lo¶l{�âr l�tL�I�ÐvÑ�Ê��bs�� �K}AoÇ�le?bdcfee?jkh?cie1qK¯ � �:»Âe?qfe�osu~u{h�jkh)glb.y~n8�osqdosbdo�r3e1qfe�j�e?nleh¢'uwe�ÄÅ}Agljsy��h)gu�tL��vNr � � � ­� � |âx �¡ �y|~tL� � vüoã|~t�� � o»��v �  

Óx��±Kywe?z|osg�cfo<¯ � råu�t�¯ vÑ���]nlosz��e?b�okbxÄ1�e?jsy~u©jsh)z|rlq.h?�3e?q5�K}Ao�uut ¢�vsr unm�tY¢�vòr�¢U�� unm m�t���v�nßÔ¢*m¤àI� ���Ðb.}Ar�� | m m�� �O»Bh)qÉuwe�Ä1�h)q.z�}luwe�nAo%�Âe��Ku{h)qpjkh)g�okq.qdh)qÉb.o�cfy~osglo� u�tL��v���ßÔ¢ m ¡{à � ��� ÷3b.}lr·� | m m � z

nlo*nlh?glnlo*b.o*nloknl}ljso�uwe�okbdcfy~z�e1jsy��h?g�r3e?qfe�¯ � �ÌÎÍ ê3ë{ü°ëÍ�°ë tÏÓxz|y~c.y{nlh�vÑ�ÌÎÍ ê3ë{ü°ë � ë tÏÓxz|y~c.y{nlh�vÑ�ê3ë¤�Bë ê3ë Æxokq.y~±1e?gAnlh�uwe�osjk}3e?jky��h)g

l m m r ¡*lVoË¡#�Il m r ¡*lVo\�{� q l�� lnm m¡ { rÙtm£Zo�¡� q v�l  

Æxo�u{e�z|y{bdz�e%ÄÅh)q.zUel m m m r ¡*l m oPî*�Il±o��{� q l m r �*�Il}oPî*�Il±oPî*�I÷Úl�� l m m m× { r ¡�Ilut�×�o�¡#� q vР

²`h���}lo�nle�u~}l��e?qÈe|u{e�y~cfokqfe?jky��h)g�nAosu`osg�}lgAjsywe1nlhl�ê3ë¤�Bë~ö°ë Æxokq.y~±1e?gAnlh�nlh)bp±)okjsokb�uwe�okjs}3e?jky��h)g�l m rp|~t���z�lvÑ�Abdo�h)�Zcfy{okglo

l m m r}| � oP| � l m r¿| � oã| � |l m m m r}| ��� oã| � � l m o¿tÇ| � � oã| �R� l m v�|hoP| � tÇ| � oã| � l m vr}| ��� o�¡4| � � |·oã| �R� | q oã| � | � oã| q� |²`uwe1z�e?gAnlhâë �§Ð q ��ë �1Ð ÷ e�osbdcfe?b�o�µZrlqdosbdy{h)glokb�bd}lbdc.y~c.}A�)okglnlh��"o0l�r^h)q±� � o0l � �`osuz\�okc.hZnlh�nAo%�Âe��Ku{h)qÉosbÉnlo*u{e�ÄÅh)q.zUel � � � rÈl � oP¯I|~tL� � z�l � vüoaë �1Ð q ¯q¡ { oPë �§Ð ÷ ¯ ÷× {  

��×

Page 52: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ê3ë¤�Bë~ü°ë ºZose\okuxrlqdh)�lu{okz�e�l m r |~t���z�lv�jsh)g�lpr tLl � z¡l q v ­ �±|�r t�| � zÐ| q v ­ ��]rlu{y~j�e?glnAh�uwe�q.ok�)uwe�nlo*u{e�j�e?nlokg3e

ì l��lnqÚð m m r ì | �� | �� � | �� �|]q� |]q� � |]q� � ð ÊÌ £t�l���vÌmt�lnqÚvÌmÍÏ r ì | �� oã| �� � | � oã| �� � | q|]q� oã|]q� � |��uoã| q� � |]qÚðºZose?g¶ëH��§Ð q �âë�q�§Ð q u{e?bÈjshKh)qdnlosg3e1n3e?bÉnlo*osbmcfo�±)okjkcfh?q]e1u°b.}lbmcfyªcf}ly~qÂ�©��lI�:o}lnqpr^h?qs� � �l��� o}l7q� ¸3osg�cfh?gljsokb]oku`z\�o�cfhKnlh�nlo*�Ge��Ku{h)qpokbì l �� � �l q� � � ð ríì l ��l q� ð o ì | � tL� � z�l �� z�l q� v| q tL� � z�l �� z�l q� vyð ¯�o ì ëH��§Ð që q�§Ð q ð ¯q¡  

ê3ë¤�Bë¤�©ë e�vvÆxosqdy~±1e?glnlhVØ�±?osjkosbs�nl � � � � r O l � � nlopnAh)glnloÉy{gAnl}ljkc.y~±1e?z|osg�cfoÂl � � rO � l���a�u`z\�o�cfhKnlh�nlo*�Ge��Ku{h)qpbdosql�el � � � r�l � oP¯ O l � o ¯q¡ { O q l � o ¯ ÷×!{ O ÷Úl � o������o ¯ �ØO{ O � l �  Á �IvɺZy�Øhr� �3bdo*c.y{okglo

l � � � rÈú > �]l � r¿ú?� ß � �Ì� � Ú ��l �  »Bosq.h³uwe#bdh)u{}ljky��h)g\oѵle1jkcie´nlo¶lnmòr O l>osbhl�tL�]v¥ríú � ß � � � Ú � lut��I�Ðv��:r�h)q�cie?g�cfh´b.ojk}lzUrAu{oVl � rÈl�tL� � v��ê3ë¤�BëÍ�°ë t ¹�e?y~q.osqprP��à?¢�ve�v5¬�h)z|h Ê m�À ¢A� Ê osbx}lgle|ÄÅ}lgljky��h)g�osbmcfq.y~jkcfe?zUokg�cfo%jsq.okjsy~osg�cfo1�Pr�h)q]h1cfq.hUuwe?nAhl�ý�� 0� ú � ­ � ë4�Nr�� ç � °)¡]y{z|rlu~y{j�eÈ��}lo�osbGbdh)�lqdok�)okjkc.y~±1eA�v�]b��� rA}losbGc.y{okglo8}Ag3e]ÄÅ}lgljky��h)gy~g�±?osqdbfeÛl�r;l�tL�]v��Ç»Bh)q�u{eÇqdos�)u{eÇnloUnlosqdy~±1e?jky��h)g³nloUÄÅ}lgAjsy{h?glosb�y{g�±)okq.bfe1b�lnm tL�]v.r£° Ê t�l�tL�]v�v��¥u{h5��}lo�n3eÉu{}A��e?qBe5u{e5okjs}3e1jsy��h?g�nlyªÄÅosq.okgljsy{e?u�nlokuKokg�}lgljsy{e?nlhl�Ga�bÂo�±Zy~nlosg�c.o��}lo}l�tY¢�vNr ¢A��IvpÆxosqdy~±1e?glnAh�uwe�osjk}3e?jsy��h)g

l m m r.ç � ú�� � l m l·r � ¡ l7ú q � �l m m m r � ¡ l m ú q � � o � ¡ l7ú q � � �{l7l m r � ÷ ��q� új÷�� � tУÂo\�4l q vÄ �)�

Page 53: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

»Bh)qÉjsh)glbdy{�)}Ay{osg�c.o�osu`z\�okcfhKnlh�nlo*�Âe��Ku~h)qp�l}lbdj�e?nlhUosbl � � � r¹l � o ç �¡ ú ���� ¯.o � � l � ú q ���� ¯ q o � ÷ ��q¡1� ú ÷����� tm£Do��{l q� v¡¯ ÷  

ÌÎÍ ê3ëè�©ëÍ�°ë tÏÓxz|y~c.y{nlh�vÑ�ê3ëÍ�`ë ê3ë ¬�h)gAb.y{n8�osq.okb.o1��rle?qfe�b.y~zUrAu{y~Álj�e?qk�Ab3�h?u{h�osu`jse?b.h|osbdj�e?u{e?qs�O­<�h?cfokb.o%��}lo

l m rÈ| z l m m r¿| � oP| � l m r¿| � oã| � |I »Bh)qpcie?g�cfh�oku`r^h)u~y{glh?zUy~h�nlo*�Âe��Ku~h)qpnlo*�)qfe1nlhU¡�nAo(l�tL��oã¯Iv�x l�tL�]v�okg�¯wr ¢�osbl�tL�]vüoP|u¯ÅoÈtÇ| � oP| � |uv ¯ q¡  ��y~osg�cfq.e?bÉ��}lo*osu`nlo*�)q.e?nlh�£�nAoÅ|�tL��oã¯uz�l�tL�Åoã¯Iv¡vÈokb

|·o¿t�| � oã| � l m v¡¯wrp|0o¿tÇ| � oP| � |uv¡¯u Æxo�e?��}°�� ��u{h)b�jkhZo�Á3jsy~osg�cfokb�nlo��Ge��Ku{h)q�nlo��)qfe?nAh)b�£���¡<osgã¯�r ¢�nlokuÈosqdq.h)q�nloc.q.}lgljse?jsy��h)g�b.h)g@ � r¿|wx»¸�|¥x º�|Iz @ q r £¡ tÇ| � oP| � |uv�x»¸ÂtÇ| � oP| � |uvÄ »Âe?qfe%�K}Aoxosu�h)q.nAosg�nlo]jsh)gAb.y{bmcfokgljsy{e�b.ose�£x�3e1bdcie%jsh)g��K}AoV¸0o�º�r £?��� rle?qfe���}lobdo�eU¡�¦le����K}Ao�y~zUr�h)glokqpe?nlokz+�e?b�£�°)¡±x»¸Jr ¢A�3okb5nAosjsy~qs�I¸JrȺ�r�£°?¡Z�

ê3ëÍ�`ë~ö°ë e�vp¬�h?zUh�okg�oku`rlq.h)�Au{oszUe�e?g�c.osq.y~h)qs�Aglh)bÉu{y~zUyªcie?qdosz|h)b:e?u°j�e1b.h|osb.jse?uwe1qs�a�u`r�h)u{y~glh)z|y{h%nlo*�Ge��Ku{h)qÉnlo*�)q.e?nlh�£*nlo.|~tL��o > � z�l±o > � |~t���z�lHv¡v�osgÛ¯wr ¢�okb|·o¿t £ï | � o £ï | � |uv¡¯u 

¬�h)z|r3e?q.e?glnlh�jsh)g�okuAnlokbfe?qdq.h)u~u{h�nAoÈ�Ge��Ku{h?qGnloòl�tL�Now¯Iv�x0l�tL�]vDtű��o�e1b.oposuZrlq.h?�lu{okz�ee?g�c.osq.y~h)qÚvÑ�©b.oUc.y{okglo��K}Ao�u{h?b%jkhZo�Á3jsy~osg�cfokb�nlo|�Âe��Ku~h)q*nlosuOosqdq.h)q%nlo�cfqd}lglj�e1jsy��h?g³nlo�)q.e?nlh)b�£*�Ç¡�b.o%e?g�}lu{e?g@ � rp|0o à¡ |wx ï¡ |¶r ¢Hz @ q r £¡ t�| � oã| � |�v1x ï¡ t £ï | � o £ï | � |uvNr ¢H ��à

Page 54: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

­5h�osbpnlyªÄm�� jsy~ul±)okqs�3b.y~g�¦3e?jkosqÈu~h)bÈj`�e1u{js}Au{h)bk�Z��}lo�oku°nlox�)q.e?nlh·×�gAh�b.o*e?g�}lu{eA�Z�)e���}lookg�osu�jshKokÁljsy{okg�cfo5jsh)qdq.osbdr^h?glnly{okg�cfo�nAo3l�tL�/oJ¯Iv x¶lut��]vGglh�e?rle?q.okjsosgUr^h1cfosgAjsywe1b8nloï�okgÇoku°nlokglh)z|y{g3e?nAh)q8��osg�osuPnlo(|~tL�.o > � z�l/o > � |~t���z�lv�v:bs�� e?r3e?qdosjkosg°�:»Âh?qÈcie?g�cfhoku`h)q.nlokg�nAo%jkh)glbdy{bdc.osgljkywe�osb�¡���glh|z�e��?h)qs��Iv*¬�h)z|h�osuOz\�o�cfhKnlh�osb%h)��±Kywe?z|osg�c.o|jkh)glbdy{bdc.osg�cfo1�G�3e1bdcie�glh?cfe?q���}lo|uwe�jsh)z��r�h)b.y~jsy��h)g�nlo�ÄÅ}lgljky{h)glokb5²©y~rlb.ji¦Ay~cfÃ�okb5cfe?z��ly��osg�²`y{rAb.ji¦lyªcfÃ?�ê3ëÍ�`ë~ü°ë e�v��]u`nlosb.e?q.qdh)u{u{e?q $ r�h)qp�Âe��Ku~h)qposgÛ¯wr ¢�¦3e?bmcie��)qfe1nlh�£%bdo�cfy{okglo

|·o¿t £¡ | � o £¡ | � |uv¡¯u 

a�u�r^h?u{y{gAh)zUy~hxnlo]�Ge��Ku{h)q:nlo5�)qfe1nlh�¡*nlo/l�tL�/oJ¯Iv x¶l�tL�]v�osbò|�¯eo»t�| � oJ| � |uv�¯ q °)¡Z�jkh)g�u~h�js}3e1u`osu`h)qdnlosgÇnlo*jsh)gAb.y{bmcfokgljsy{eA�l��r�h)qÈcie?g�c.h|oku`nlo*jsh)g�±?osq.�?osgljkyweUokb]¡Z��IvÈ��rAu{y{j°�e?glnlh?u{h�e0l�m7r¹�Iq��l�tY¢�vNr ¢A�3b.o�cfy~osglol � � � r¹l � oP¯�t�� � o ¯

¡ v q z l{�Âr ¢H ®Òc.osqfe1glnlh|jsh)g�� � r¹¢u¯`� ¯¥r�£°Tû´�

l4½»r]� £¡ � q ¯÷�o � × ¡ � q ¯÷�o¹������o �Ìû²x £¡ � q ¯÷r £

��û ÷ tm£ q oa× q o�������oÈtÏ¡{û x+£v q vr £��û ÷ � î{û ÷ x�¡{ûÕ r £× x £

£¥¡{û q r�lutУv1x ¯q£¥¡  ¬�h)gÇu{h�jk}3e?u`u~y{z > ­ � ¯ � É � lutУv�x l{½}�*rc r3e1qfe Ê ÀÔ¡Z�

ê3ëÍ�`ë¤�©ë t ¹�e?y~q.osqprP�)��à4ve�vȲ©e�q.osjk}lq.qdosgljkywe�osbl � � � tL�]v�r £Do �� l � tL��vNë4�Ðz

��}lo%e�r3e?qdc.y{qÈnAo(l � ì £*rlqdhZnA}ljsol q tL�]v�r�£�o±��z l ÷ tL�]v�r&£o3�]o �Iq¡ zj T j  l � t��]vZr&£o3�]o �Iq¡ o������ o � �*� �tL¢âx�£v�{ zokb5nAosjsy~qs�3u~h)bpr^h?u{y{gAh)zUy~h)b:nlo*�Ge��Ku{h)qpnAo%u{e�o�µZr�h)glosgAjsywe1u`osg��¶r ¢A�

��Õ

Page 55: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

� �Ivp²©e�Ä1�h)q.z�}luwe�nAosu©z\�o�cfhKnlh�nlo%»�y{jse?q.n�y{z|rlu~y{j�e� l � � � tL�]v~xAl � t��]v��ß �ÿ � |~tL�Ðz�l � tL��v�vNx |~tL�Ðz�l �*� � tL��v¡v��*ë��ß3ª �ÿ � l � tL��v�x l �#� � tL��v��#ë4�

nlh?glnloZª�okbBu{eÈjsh)gAbdcie1g�c.o:²©y~rlb.ji¦Ay~cfÃ�okg�u{eÈb.ok�)}lgln3ep±1e?q.y{e?�lu~o?�©»Ge1qdcfy~osglnAh5nAoZl � ì 4��bdo�c.y{okglo�l q t��]v¥rê4?o�tL�Jx¹�nvRø>��nAh)glnlo�ø okbU}Ag3e´jkh)glbmcie?g�cfo1��²©e´e?jsh1cie?jky��h)ge?g�c.osq.y~h)qpy{z|rlu~y{j�eZ�Kyªcfokqfe?glnAhl�� l � � � t��]v~x l � tL�]v��7ß�ª �#� � ø � �?x �u� �¢�{  

a�gÇr3e?qdc.y{jk}luwe?q�uwe�b.okq.y~ol � t��]vüo 0B �32 � tLl � � � tL�]v�x l � t��]v¡v

jkh)g�±)osqd�)o�}lglyªÄÅh)q.z|osz|osg�cfo�tÅcfokbdcJ� nlo�¿³osy~osq.bmcfq.e?b.b�v�e#}lg3e#ÄÅ}lgljky��h)g l�tL�]vÑ�³²©e?bbd}lz�e1b#r3e?qdjsywe1u{osb�nloÊosbmcie�b.okq.y~o>b.h)gÝl � t��]v���jkh)g�u{h�js}3e?u��K}Aosn3e�rlqdh)�3e?nlh���}lol � t��]vZ¾ l�tL�]v�}lglyªÄÅh)q.z|osz|osg�c.o?�Oa�bdc.hUr�osqdzUyªcfo�c.h)z�e1qÈuÒ�� zUyªcfosb8osgÇuwe�q.okuwe?jky��h)gl � � � tL�]v�r�lut��7vüo �ÿ |~tL�Ðz¡l � tL��v�v~ë��Ðz

bdy{osz|rlqdo%��}loÅ|�b.o�e�jsh?g�c.y{g�}3eA��Æxo*nlh)glnlo}l�okb]}lgle|bdh)u{}ljky��h)g�nlo(l�mr¿|~tL��z�lHv�jsh?gl�t��nvNr�4�r^h)qd��}lo.l � t��nvZr54^�a�b�nlokjsy~qs�Gbdo�¦3eÇrlq.h)�le?nlh<��}lo�b.yÂ|�osb�jsh)g�c.y{g�}3eÇ�³²`y{rAb.ji¦lyªcfÃ�okg"u{e�b.ok�)}lglnle±1e?qdywe?�lu~opb.o5cfy{okglo5o�µZy{bmcfosgAjsywe�nlo�bdh)u{}ljky��h)g|osgUosu�rlq.h?�lu{okz�e}lnm7r¿|~tL��z�lHv���l�t��nvNrc4��²©e�}lgly~jsy{nle?n�b.o�rl}loknlo�h)�Ac.osglokq*e�r3e?qdc.y{qxnAo�}lg3e�e?jsh1cie?jky��h)g�jkh)zUh�uwe�y{gAy{jsy{e?uÏ�r�h)q.��}lo*bdy`¦K}A�ly{okqfe�nlh)bÉb.h)u~}ljsy~h)glokbpnly{bmcfy{g�cfe?bstNl�� ¤l��lb.o%js}AzUrlu~y{qs�� ebd}lr­�� ý ÿ Ð � þ � lut���v1x ¤l�tL��v���ß�ªV� �wx �u�:b.}Ar­�� ý ÿ Ð � þ � lut���v1x ¤l]tL��v� z

u~h"js}le?u]okb�}lg3e>jkh)g�cfq.e?nly{jkjsy��h)g�r3e1qfeAª±� �\x¿�ü� æ £)�posb�nlosjky{qs�pokg�}lg+r�os��}lo� gAhokg�c.h)q.gAhUnlo(�3�:¬�h)gÇu{h�js}le?uÏ�lu~hZjse?u{z|osg�c.o?�A¦le���b.h)u~}ljsy��h)g��}lgly{jseA�ÌÎÍ ê3ë��°ëÍ�°ë tÏÓxz|y~c.y{nlh�vÑ�

��ï

Page 56: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÌÎÍ ê3ë��°ëÍ�°ë tÏÓxz|y~c.y{nlh�vÑ�ê3ëÍ�`ë ê3ë ¬�h?g�u{hp±Ky{bmcfh]¦3e?bdcfe]e1¦lh)qfeZ�1okuKzÊ�okc.hZnAh5nAo�a�}lu~osq©zUhKnlyªÁ3j�e?nAh5okbx«mzUoE·dh)q.¯��}loÈu{e5qdos�)u{e]nlokuKc.qfe?r�osjky{h]r^h)qd��}loÈosbGnlosuKzUy~b.z|h]h?q.nlokg��%osbvoѵArAuÒ�� jky~c.h�t ��r�h)qBcie?g�cfhjkh)zUrA}Acie?jky{h)gle?u{z|osg�cfo�z+�e?bpbdosgljky{u~u{h�vÑ�a�b.jkq.y{�Ay{osgAnlh

Ø � r¿|~t�� � z�l � vÄz Ø q rp|~tL� � oůüz¡l � o ¯ ¡ Ø � o ¯ ¡ Ø q vÄz l � � � r¹l � o ¯ ¡ tÇØ � oÅØ q vÄzbdoxcfy{okglo(Ø q r ¡t�l � � � x�l � v1x ¯I|~t�� � z¡l � v��l��}lo*bd}lbdc.y~cf}Z�)osgAnlhUokg�uwe�Ä1�h)qdz�}luwe�r3e?qfeØ q y{z|rlu{y~j�e ¡t�l � � � x l � v�x»¯I|~t�� � z�l � vNr¿¯ |�tL� � � � z�l � � � vu~h��K}Ao�nlokb.rl}8�osb5nlo�h?r^okqfe?qpn3e�u~}l��e?qÉe�uwe�qdos�)u{e�nlosu°c.qfe?r�osjky{hl�

ê3ëÍ�`ë~ö°ë a�u`z\�okcfhKnlh�osg�cZ�okq.z|y{glh?bÈnlo*u{h)beØ,�BosbØ � r}|~t�� � z¡l � vØ q r}|~t�� � o ¯ × z�l � o ¯ × Ø � vØ ÷ r}|~t�� � o ¡{¯× z¡l � o ¡4¯× Ø q vl � � � r±l � o ¯

� tÇØ � oP×4Ø ÷ v»Bh)qpcie?g�cfh�oku°cie?�lu~osqdh|okb

¢£°{× £°{ס4°{× ¢ ¡{°{×£°1� ¢ ×4°1�ê3ëÍ�`ë~ü°ë �]u©e?rlu{y~j�e?qdu{h�jsh)gÛ|~tL��z¡lvNr�l�b.o*h)�Ac.y{okglo

l � � � r¹l � o ¯ � �Çl � oP× �Çl � o ¡4¯× t�l � o ¯ × l � v �Z�r8�i£ZoP¯�o ¯q¡ o ¯ ÷ÕJ� l ���î

Page 57: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

»Bh)qpcie?g�cfhl4½ r � £Zo�¯Åo ¯q¡ o ¯ ÷Õ � ½ r � ú > oaÆwtǯ " v � ½ r¿ú � > � £DoaÆwtǯ " v � ½rVú � ø �.£ÂoaÆwt�û�¯!"6v � rÈú � ø �i£DoaÆwtǯ÷Ðv �  �]b��� rl}lokbh� l4½\x lut�� ½Âv��*r¿Æwt�¯ ÷ v��

ê3ëÍ�`ë¤�©ë e�vÈav±Ky{nAosg�cfokzUokg�c.oX�I¥t�\Ø m v�xvI?t�\Ø7vZX3ß�EBzUeMµ� X�I � t�\Ø m v�x�I � t�\Øv3X »Bh)qpcie?g�cfh�oѵAy~bdc.o%jky{okqdcfh�D�cie1u°��}lo?��r�h)qpb.okq3|'²`y{rlbdji¦ly~c.Ã?�X�I?t \Ø m v�xvI¥t \ØHv3X±ß�E�ªrX6¯ AB ¬ 2 � �C� ¬ tÇØ m¬ x»Ø ¬ vZX ­<�h?cfokb.o���}lo?Ønm¬ zÚØ ¬ ¦ §MF��`b.h)g�±?osjkc.h)q.okbs���]rlu{y~j�e?gAnlh�uwe�nAosb.y~�)}3e?u~n3e?n#nAo|¬Èe?}lji¦����ºZji¦ ��e?q.Ã�e�j�e?n3e�}lgle|nlo*u{e?bpjshKh)q.nAosg3e?nle?bÉnlo�« A¬ 2 � �C� ¬ tÇØ m¬ x»Ø ¬ v��3bdo%nAosnl}ljkoX8AB ¬ 2 � � � ¬ t�Ø m¬ x»Ø ¬ v3X3ß � AB ¬ 2 � �C� ¬ � B ¬ X6Ø m¬ x»Ø ¬ X q

ß�E©z�e¥µÅ� � � ¬ � q X¢\Ø m x�\ØÑX q  aGµKcfq.e��?osglnAh�qfeA�� jsokb5jk}3e?nlq.e?n3e?bÉ��bd}lbdc.y~cf}Z�)osgAnlhl��b.o%u{u{ok��e�e�zUoE·dh)qfe?qpu{e�jsh)glbmcie?g�c.o²`y{rAb.ji¦lyªcfÃ�nloku`osg�}lgljkywe?nlh|osgÇ}lg�Ä e?jkc.h)qHE*����q���IvpºZok�È�}lg�osuPrlq.y~zUokqÈe?r3e1qdcie1nlhl�Arle?qfeh¯ æ E � q ª � � °vzUeMµ.� �C� ¬ ��uwe�ÄÅ}Agljsy��h)g�cfy~osglojkh)glbdcfe?g�cfo�nlo#²©y~rlb.ji¦Ay~cfÃ�zUokglh)qU�K}Ao�}lglhl�p�Ër^h)qUosu5cfosh?q.oszUe"nlo<uwe>e?rAu{y{jse?jsy��h)gjkh)g�cfqfe1jkcfyª±1e�nAos��o%oѵZy{bdc.y{qp}lg��}lgly~jsh�rl}lg�c.h|Á1·dhA�

ê3ëÍ�`ëÍ�°ë ­#�h?c.osb.o���}lo�r3e?qfeU¦3e?u{u{e?q3Ø � ¦3e��<��}lo�qdosb.h?u~±)okqx}lg3eUosjs}le?jsy��h)g�nlosuBcfy~r^hØ � r I � tÇØ � vÑ�x�]gleU±)okÃ�q.osbd}losuªcieA��b.o�rl}losnAo�¦3e?u~uwe?q/Ø q q.okb.h)uª±Ky{osgAnlh�h?c.qfe�okjs}3e?jky��h)gnloku�z|y{bdzUh�cfy~r^h)t r�h)q.��}loâØ � osb��)e#jsh)glhKjsy~nlh�vÑ�Gokc.j?��a�b�nAosjsy~qs�vokgÊj�e?nle<j�e?bdh�uweokjs}3e?jky��h)g)t okg<�)okglosq.e?u©glh|u{y{gAo�e?u v8��}lo�¦3e�����}lo%q.okb.h)uª±)osqÉcfy~osglo%nly~zUokglb.y��h)g¶ë�y{�)}le?ue?u©g��}lz|osqdhUnAo�jshKh)qdnlosg3e1n3e?b�nAo�u{h?b±Ø,�Ò�]ºZy~g<okz��3e?qd�)h�okg#u{h)bÉz\�okc.hZnlh?b]y~zUrluÏ�� jky~cfh?b�)okglosq.e?u{okbG¦3e�����}loÈq.okb.h)uª±)okqv}lg�bdy{bdc.oszUe�nlo8nly{z|osglbdy��h)g�E�ë��1u{h]�K}AoÈjsh)z|rl}Acfe?jsy~h)g3e?u �z|osg�cfo*okb5z��e?bpjkh)bdc.h)b.hl�

��ñ

Page 58: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÌÎÍ ê3ë��°ëÍ�°ë tÏÓxz|y~c.y{nlh�vÑ�ê3ë � ë ê3ë ²©e?bÉjsh?glnly{jky{h)gAosbpnlo*h)qdnlosg´£��Ç¡�bdo*osb.jkq.y~�^okg�qdosb.r�osj�cfyª±?e1zUokg�c.o*jsh)z|h\¼D� \£3r�£ � ¡ \¼ ­ O \£3r�£tÅgÉ�h?cfokb.o���}lo O \£�osb�oku±)okjkc.h)q�js}A�)e�jshKh)q.nlokg3e?n3e<NIx��osbdy{zUe�osb³« � � ¬o� vÑ�*»Âh)qxh1cfq.hu{e?nlh × B ¬ Ð � Ð ë ¼ ¬ � ¬R� � ¬ ë�r £�� × B ¬ Ð � Ð ë ¤ � � ��¼�� ¬ � ¬ ë�r £{z

nlh?glnlo ¤ � � �]r¿� � �Pb.h)g�u~h)b:osu{okzUokg�cfh)b8nlo O/­ ��okg�cfh)gljkosbpu{e?b8jkh)glnly~jsy~h)glosb8nloxh)qdnlosg�×bdh)g°�3jsh?g�okbdcie�glh?cfe?jsy��h)g°�× \£ ­ O ­ ^ O \£3r�£ � Õ \¼ ­ O q \£/r £4 ê3ë � ë~ö°ë e�vÈa�u°cfe?�lu{okq.h�osb

£°?¡£°?¡ ££°)¡ £°)¡� osbmc��e�e%uwe�±Zy~bdcfe���}lor@��^glh�okb�uwe*b.}Az�e%nlo�u{e*Á3u{eYD�x��okb.y~z�eA�jD�r £4zi¡Z��a�u�h)q.nlokg�b.onlok�^o�j�e?u~js}lu{e?q]jkh)g#u{e�nlokÁlgly{jky��h)g�r^h)qd��}lo�b.o�rlq.h)�le?q.h)g�u{e?b5jsh)glnAy{jsy~h)glokb�nlo�h?q.nlokgjk}3e?glnlh%b.o5bfeMcfy{bmÄ e?j?�� exuwe�jsh?glnly{jky��h)g�nloÉbd}lz�e*r�h)qvÁ3uwe1bs��Æxokbfe?qdq.h)u~uwe?glnAhxr^h?q:�Âe��Ku{h)qokg�¯wr ¢Ø��� r¿| ��o £

¡ | �� ¯ÅoPÆwt�¯ q vÄz Ø��q rÈ| ��o¿t £¡ | �� o B ! | �! | ! v�¯ÅoaÆwtǯ q vnlh?glnloV| ! y~glnly{jse%u{e�nlokq.yª±?e1n3e�nlo±|Çjkh)g�q.okb.r�osj�cfh�e�u{e<øAx��osbdy{zUe�jsh?zUr�h)glokg�c.o�nlol���»Âh?q5h1cfqfe�r3e1qdcfo

l"�Ht�� � oã¯Iv�x l"�HtL� � v�r¿| �{¯Åo¿t�| �� o B ! | �! | ! v ¯ q¡ oaÆwt�¯�÷ÚvÄ ²`hÇjs}3e?uOjkh)y{gljky{nlo�¦le?bdcfe�h)qdnlosg>¡�jkh)g > q t�Ø �� oÈØ �q v��U��bs�� rl}Aosb�¯ � räÆ¥tǯ ÷ v��'osuh)qdnlosgÇosb]¡Z��Ivp�]gÇj`�e1u{js}Au{h�b.y~zUy~uwe?q8e?u`e1g�c.osqdy{h)qprlqd}los�le|okg�okbdcfo%j�e1b.hØ��� rp|#��o @ � | �� ¯òo�Æwt�¯ q vÄz Ø"�q rÈ| ��o t}@ q | �� o tÏ¡*º1v�� � B ! |#�! | ! v¡¯òo�Æwt�¯ q vÄ 

à?¢

Page 59: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

»Âe?qfe*��}loV¯�t�¼ � Ø �� o�¼ q Ø �q v�jsh)y~gljsy~n3e�¦3e?bdcfe�h)qdnlosg�¡*jkh)g¥l � t�� � o�¯ v�x�l � tL� � vOnlok�^ojk}lzUrAu{y{qdb.o1�Ar�h)qpcie?g�cfhA�¼ � oP¼ q r £4z ¼ � @ � oP¼ q @ q r £

¡ z tÏ¡*º1v�� � ¼ q r £¡  

Æxo�nlh?glnlo*b.o%nlosnA}ljso¼ � r&£ex º�z ¼ q r¹º�z�@ q r�t £¡ x¹tm£òx º1vo@ � v�°*º

jkh)g�@ � e?q.�lyªcfq.e?q.y~h�js}lz|rlu{y~osglnAh�@ � Ãr ¢|rle?qfe���}lo*glhUbdo%±?osqdy~Á3��}lo%uwe�jsh?glnly{jky��h)g�nlobd}lz�e�r�h)qÈÁ3u{e?bs�j�v�»Bh)q.��}lo�cfy~osglokg'osu�z|y{b.z|h�h)qdnlosg���bdh)g´y{�)}3e1uGnlo�bdy{z|rlu{okbxjsh)z|rl}Acfe?jsy~h)g3e?u �z|osg�cfo1�ê3ë � ë~ü°ë e�v�ÆxoUuwe�nAokÁ3gly~jsy��h)g Ø,��r²|~t�� � oc@��L¯uz�l � o¿¯M« ¬ �C� ¬ Ø ¬ vÑ�vb.o�nlosnl}Ajso?�okg�c.osglnAy{osgAnlhwØ,�Bjsh?zUh�ÄÅ}lgljky��h)g�nlo.¯

Ø,�ytY¢4vNrp| z Ø m� tY¢�vNrÈ| � @��Ho B ! | ! B ¬ �C� ¬ | !  Óx��±Kywe?z|osg�cfo(Ø,�ÌtY¢�v�r¹l�mLt�� � vÑ�l��« ¬ �C� ¬ r�@��©bdy`��b3�h)u~h�b.y�Ønm� t ¢�v�r¹l�m mLt�� � vÑ��Iv�²©e�ÄÅ}Agljsy��h)g�b.o�ok±1e?u1�}3e*osg�rA}lg�cfh)bÈnAoxuwe�ÄÅh?q.zUe¥t�� � o�@���¯uz�l � o)¯G« ¬ �C� ¬ Ø ¬ v��²©e�bdos�)}Agln3e<jkhZh)qdnlosgle?n3e�bdo�e?rAq.h�µZy{zUeǦ3e1bdcie�h)q.nlokg"}lgAh»t �3e�·dh<uwe�¦ly~rÉ�h?cfokb.y~b�nlou~hZjse?u{y~Ã�e?jky��h)gIv�r^h?q¶l�tL� � v�o�¯G« ¬ �C� ¬ |B�xzUy~osg�cfq.e?b���}lo"u{e\ÄÅ}lgAjsy��h?g o�±?e1u{}3e?nle�okgu{e´rlqdy{z|osq.e'jkhZh?q.nlokg3e?n3eA�Âlut�� � o @��L¯Iv���b.o#e1rlq.h�µZy{zUe�r^h)qhl�tL� � vÂopl�m�t�� � vR@��L¯Èrl�tL� � vüoã¯�@���|Â�

ê3ë � ë¤�©ë t ¹�e?y~q.okq�r°�3£s��¡4v*²Be�jsh)glnAy{jsy��h)g"nAo�h)q.nAosg�£�bdo�js}lz|rlu~oUcfqdy~±Kywe1u{z|osg�cfo1�z|y{okg�c.qfe?bG�K}Ao]u{exnloph)q.nAosg�¡�y~zUrAu{y{jseG@ ÷ r�£°)¡Z�G­]y{gA�)}lglh�nloÉokbdcfh?b:zÊ�okc.hZnAh)bvcfy~osgloh)qdnlosgd×���e���}loÅ× « ¼ ¬ @Ðq¬ Ãr�£)�ê3ë � ëÍ�°ë a�gÇosu`rlqdy{z|osqÈjse?b.hl�3u~h)bÈcie1�lu{okq.h)bpbdh)g�nAo%u{e�ÄÅh)q.zUe@ �@ q ¸¼ � ¼ q

²©e�jsh)gAnly{jky��h)g�nloÉh)qdnlosgÇ£]y~zUrAu{y{jse±¼ � o¶¼ q r�£É��u{exnlo]h?q.nlokg�¡Z�K¡*¸�¼ q r�£)�O¬�h)g|u{hjk}3e?u3cfhKnlh)b:u{h)bOz\�okc.hZnlh?b8nlo5osbmcfo5cfy{r�h%nlo��h)qdnlosgAosb�£5�U¡%qdosb.r�h)glnAosg�e%u{h)b�cie1�lu{okq.h)bàZ£

Page 60: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

¢¸ ¸¼ � £�x»¼ �¢¸ ¸£�x �q � �q �»Ge1qfe�}lg�zÊ�okc.hZnAh�y{z|rluÒ�� jsy~c.h�nlo*}lgle�o�cie?rleA�@ � @ �¼ �

u{e�jsh)glnAy{jsy��h)g�nlo*h)q.nAosg´£%y~zUrAu{y{jseż � r�£*��uwe�nlo*h)qdnlosg<¡�y~zUrAu{y{jse<@ � r�£°)¡Z�ê3ë � ëÍ�°ë a�u`z\�okcfhKnlh�osbÉnlo*h)qdnlosg�e?u°z|osgAh)b]¡�r�h)qd�K}AoB ¼ ¬ r £

¡ o £¡ r�£ � ¡ B ¼ ¬ @ ¬ r ¡ � £¡ � £� o £

¡ � ×� � r&£4 ��glh|osbÉnlo*h)qdnlosgd×�r^h)qd��}lo

× B ¼ ¬ @ q¬ r¿× � £¡ � £� q o £¡ � ×*q� q � Ãr £{ 

ê3ë � ë � ë ²©e?bÉjsh?glnly{jky{h)gAosbpnlo*h)qdnlosg´£��Ç¡�bdo*q.osnA}ljsokg#e�}lgÇj`�e?u~js}lu~h|bdosgljky{u~u{hB ¼ ¬ r £¡ o £

¡ r £ � ¡ B ¼ ¬ @ ¬ r ¡ � ×eo ç ×£¥¡ o ×eo ç ×£¥¡ � r&£4 ²©e'jsh)glnAy{jsy~h)glokb|nAoÇh?q.nlokg�×'u{u{o�±1e?g\e´j°�e?u{jk}lu{h?b�}lg�r�hZjkh³z��e?b�u{e?q.�)h?bs�˺Zo�±)osqdyª�Á3jse?q3�e�u{e�rlqdy{z|osq.e�b.y~g�j�e?z��ly{h)bk�H×*«í¼ ¬ @Ðq¬ r&£)�Z�Uuwe�b.os�?}lgln3e�osg�ÄÅh?q.zUe�zUe1cfqdy{jsy{e?uÏ�Õ \¼ ­LO \@òr Õ « ¼ ¬ � ¬R� @ � r&£)�

× B ¼ ¬ @ q¬ r × ¡ �Z� ×/o ç ×Õ � q o � ×Vx ç ×Õ � q � r £{ Õ \¼ ­ O \@�r�Õ�� �q �q � ì t�×eo ç ×4v¡°1Õ ¢x ç ×�°{× t�×/o ç ×�v�°?Õ ð ì t�×eo ç ×�v¡°?Õt�×Vx ç ×4v¡°?Õ ð r�£4 

ê3ë � ëÍ °ë ÆxoVl�m7r¿|�t�lHv8b.o�nloknl}ljko.l�m m7r¿|Im¤|Â�l�m m mHrÈ| m m¤| q�o¹t�| m¤vyqÄ|Â�Z��r^h?qÈcie?g�cfhlut�� � oã¯Iv�x l�tL� � v�rp|u¯.oã| m | ¯q¡ oÈtÇ| m m | q o¿t�| m v q |uv ¯ ÷Õ oPÆ¥tǯ " vР

à)¡

Page 61: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

a�b.jkq.y~�ly{okglnlh0Ø,��r¿|�t�u1�Lv�jsh)glu1�]rÈl�tL� � vHoJ¯M« ¬ �C� ¬ |�t�u ¬ v:b.o5cfy~osglo5��}lo�oku^okq.q.h?q8nloc.q.}lgljse?jsy��h)g�osb ¯ � r¹lut�� � oã¯Iv�x l�tL� � v~x»¯ B ¬ ¼ ¬ |~t�u ¬ vÄ �]b��� ��}lo��le?bdcfe�jsh)g�jse?u{jk}luwe?q5osuÂnlosb.e?q.qdh)u{u~h�nlo��Âe��Ku{h)q]nlo�h)qdnlosg´¡�nlo « ¼ ¬ |~t�u ¬ v��bd}lbdc.y~cf}Ay{q�osgËosbmcie´Ä1�h?q.z�}lu{e#�Êjsh)z|r3e?q.e?q�u{h)b�jkhZo�Á3jsy~osg�cfokb�nloÇ�Âe��Ku~h)q�jsh)g�u{h)b�nlol�tL� � oã¯Iv~xAlut�� � vÑ�»Âh?q:nAokÁ3gly~jsy��h)g_u§�ÌtY¢�vNrÈl�tL� � v�t bdoÉosg�cfy~osglnloKu1��jsh)z|h�ÄÅ}lgljsy��h)g|nlo/¯ vÂ��nAosq.yª±1e?gZ�nlh u m� r B ¬ �C� ¬ |~t�u ¬ vüo㯠B ¬ �C� ¬ | m t�u ¬ vnu m¬u m m� r ¡ B ¬ �C� ¬ | m t u ¬ v:u m¬ oP¯ B ¬ �C� ¬ tÇ| m t�u ¬ vnu m¬ v m��}lo�y~zUrAu{y{jse?g�osg\¯dr ¢A��u m� tY¢�vòr « ¬ �C� ¬ |Â�Ou m m� tY¢4vòr�¡�« ¬ Ð � �C� ¬ � ¬R� | m |B�xÆxh)glnAo�b.obd}lr^h?glo*�K}Ao�|<�¶| m�okbdc��e1g�bd}lbdc.y~cf}Ay{n3e?bÉokgAt�� � z�l�tL� � v�v��:a�g�c.h)gljkosb5u{h)bpjkhZo�Á3jsy~osg�cfokbnlo*�Âe��Zu~h)qpnlo « ¼ ¬ |~t u ¬ v�nlo³�h)qdnlosglokb�¢Z�°£%��¡�bdh)g@Ð�sr B ¼ ¬ |@ � r·t B ¼ ¬ | m t u ¬ v:u m¬ vTt ¢�vNr B ¬ Ð � � ¬R� | m |@ q r £¡ B ¼ ¬ t�| m m t u ¬ v6t�u m¬ v q oP| m t u ¬ vnu m m¬ vTt ¢�v

r £¡ B ¼ ¬ �Ðt B � � ¬o� |uv q | m m oË¡4| m B � Ð ë � ¬R� � � ëÍ| m |uvºZ}Abdcfyªcf}A�?osglnAh�okgUu{e�Ä1�h)q.z�}Auwe�r3e1qfe�osulokq.qdh)q�nlopcfqd}lglj�e1jsy��h?g°��u{h)bÂcZ�osqdzUy~glh)b�nloph?q.nlokg£)�3¡��â×|bdo�e1gK}Auwe?ql�e?g�b.y`b.o*jk}lzUrAu{osg�u{e?bpq.okb.r�osjkc.y~±1e?b5jsh)gAnly{jky{h)glokbpnlo*h)q.nAosg°�

ê3ë � ëÍ&°ë a�u°cie1�lu{okq.h�b.okq3�e�nlo*uwe�ÄÅh)qdz�e@ � ¸ @ � x»¸@ � º @ � x º¼ � ¼ �²©e?bxjkh)glnly~jsy~h)glosb�nlo�h)q.nAosgÊ£��'¡�y~zUrAu{y{jse?g<¡{¼ � r £)�°�4¼ � @ � rÞ£?¸`nlo�nlh)gAnlo·¼ � r@ � rÞ£°)¡K��­5y{gl�)}Aglh�nlo�okbdcfh?b%zÊ�okc.hZnAh)b�cfy~osglo�h)q.nlokg\×�r^h)qd��}loh×�t�¼ � @Ðq � oé¼ q @Äqq v/r×�°M�dÃr&£)�à{×

Page 62: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ê3ë � ë ê�+`ë a�u°cie?�Au{osqdh�b.osql�e|nAosu°cfy~r^h¢@ q @ q@ q � ÷ � � ÷ q¼ � ¼ q ¼ q

²©e?bÉjsh?glnly{jky{h)gAosbpnlo*h)qdnlosg´£)��¡���×�n3e?gÇu{}l�)e?qpe�uwe?bpokjs}3e1jsy{h?glosb¼ � oË¡{¼ q r £{z ��¼ q @ q r £{z Õ4¼ q @ qq r £{z Õ4¼ q � ÷ q @ q r £4 

Æxokb.r�oз.e?glnAh¥¼ q osg�cfhKn3e?bÉuwe?b�osjs}le?jsy~h)glosb5o*y{�)}le?uwe?gAnlhl�Kb.o%u{u{ok��e�e@ q r ¡× z ¼ q r ×î z ¼ � r £� z � ÷ q r ¡×  

»Âe?qfe´�K}Ao#b.o�js}lz|rluwe´uwe'jsh)gAnly{jky��h)gËnlo<bd}lz�e´r^h?q|Á3u{e?b|b.o<nAos��o<cfokglosq�e?nlosz��e?b� ÷ � r ¢A�ê3ë � ë ê�ê3ë Æxo�Á3gly~osglnlh0Ø � r¿|~��� � o > q z � � � � � � �q � bdoxrl}loknlo�osbdjsq.y~�ly{qDl � � � xJl � r¯IØ � � Ø � rÈ|m�Ç� � o ¯

¡ z�l � o £¡ t�l � � � x l � v � r¿|m�Ç� � o ¯ ¡ z¡l � o ¯ ¡ Ø � �  

»Bh)qGjkh)glb.y~�)}ly~osg�cfo8osbG}Ag�z\�o�cfhKnlh]nAoÈ}lg3e�o�cie?rle�jsh)g�@ � r�£°?¡Z�4� �Ì� r&£°)¡p��¼ � r £)�ÌÎÍ ê3ë � ë êKö°ë tÏÓxz|y~cfy~nlh�vÑ�ê3ëÍ `ë ê3ë ²©e?b:jsh)gAnly{jky{h)glokbOnlo]h?q.nlokg�£)�A¡x�·×%bdo]±?osq.yªÁ3j�e1g�jsh?gUbdosgljky{u{u~h)bOj`�e?u~js}lu~h)b

h)q.nAosg´£�x]¾ ¡ñ o £× o � ñ r�£h)q.nAosg<¡äx]¾ ¡ � £× � £¡ o � ñ � ×��� r�£h)q.nAosgd×;x]¾ ×�� £× � £¡ q o � ñ � ×{q� q � r £

Õ�� £× � £¡ �¥¢eo � ñ � ×� � £¡ � r £

à1�

Page 63: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

²©e�jsh)gAnly{jky��h)g�nlo*h)qdnlosgÇ�|e?b.hKjsy{e?n3e�e?u%�e?qd�^h?u°u{y~glo�e?u^osb¡1� B¬ Ð � Ð ë Ð ¿ ¼ ¬ � ¬o� � � ëè� ë ¿ r £4 

¬�h)z|h�okuGz\�okc.hZnlhUosbxoѵZrluÒ�� jsy~c.hl��glosjkosb.e?q.y{e?zUokg�cfo�u~h)b�bd}lzUe?glnlh)b]glh�g�}lu~h)b�jkh)q.qdosbm�r�h)glnlokg'e_NÛÀ ØJÀ%$sÀ����%»Âokq.h�osb�y~zUr�h)bdy{�lu~o%oku{ok�)y{q]js}3e1c.q.h�okg�cfosqdh)b*osg�cfqdo�£��E/r¿×A�lr�h)qpu{h���}lo*osu`rAq.y{z|osqpz|y{okz��lqdh�b.o�e?g�}luweZ�ê3ëÍ `ë~ö°ë »Âh)q�osuPz|y{bdzUh�e?qd�)}lz|osg�cfh�nAosuPrAq.h)�lu~oszUe�e?g�c.osq.y~h)qs�Kosu�h)qdnlosg�glh�rl}losnAobdosq}àZ��»Âh)q]h?cfq.eUr3e1qdcfo1�°osb5Ä1�e?jsy~uÂjkh)z|rlq.h)�le?q]��}lo�b.o�±?osq.yªÁ3j�e1g�uwe?b5jsh)gAnly{jky{h)glokb�nloh)qdnlosg�£?�:¡Ç� ×A�'¹]e��"��}lo�jkosg�cfq.e?q.bdo?�:r^h)q�jsh)gAb.y{�?}ly{okg�c.o?��okg�jkh)z|rlq.h)�le?q�u{e?b�nloh)qdnlosgU�l��¹]e?�lq3�e*}lg3e%jsh)gAnly{jky��h)gUe?b.hKjsy{e?n3e%e%jse?n3e%}lglh�nAo]u~h)bU�e?q.��h)u{okbOnlo�h)qdnlosgU�l�

&¬ &�O r &ë &¿

&¬ &ë^�r &¿ &� &¬ &

�� r & ë &¿ &¬ &�¨=r &ë &¿

�5c.y{u~y{Ã�e1glnlh*uwe%nlokÁ3gAy{jsy��h)g°��b.o]cfy{okgloK�~t O v�r ¡M�l�j��t}^0v�rÈîA�¢��t��.vZr �l�j��t}¨âvNr£¥¡K�A�$ ¬ t O v�r B� Ð ë Ð ¿ � ¬R� � � ëÍ� ë ¿ r B � Ð ë � ¬R� � � ë�@�ë $ ¬ t}^0v�r B� Ð ë Ð ¿ � ¬R� � ¬ ëè� ë ¿ r B ë @ ¬ � ¬ ë�@�ë$ ¬ t��.vZr B� Ð ë Ð ¿ � ¬ ¿ � ¬ ëè� ¬R� r�@ ÷¬ $ ¬ tL¨âvNr B� Ð ë Ð ¿ � ¬R� � � ¿ � � ër B � � ¬R� @ q�a�g>jse?n3e<jse?b.hl�G}lglh)b�bdosgljky{u~u{h)b%j`�e?u~js}lu~h)b%rlq.}lok�3e?g>��}loJ�~t���v�« ¼ ¬ $ ¬ tL��v.r £)�G�´osuz\�okc.hZnlh�okb]nAo%h?q.nlokg��l�

ê3ëÍ `ë~ü°ë a�u{y~�)y{okglnlh�u~h)bÇ�e?qd�^h)u~osb

&¬ &�O r &ë &¿ &�

&¬ &ë^�r &¿ &�

&� &¬ &�� r & ë &¿ &�

à4à

Page 64: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

bdo*c.y{okglosgÇuwe?bpjkh)q.qdosbdr^h)gAnly{okg�c.osb5jsh)gAnly{jky{h)glokbpnlo*h)q.nAosgO x�¾ £�¡?¢ B ¼ ¬ � ¬R� � � ë¤� ë ¿ � ¿ � r £^ x]¾ ×)¢ B ¼ ¬ � ¬o� � ¬ ë¤�¢ë ¿ � ¿ � r £� x]¾ à B ¼ ¬ � ¬R� � ¬ ë¤� ¬ ¿ � ¬ � r�£¬�h)z|h�okuGz\�okc.hZnlhUosb�oѵArAuÒ�� jky~c.hl��uwe �}lgAy{j�e|jsh)g�c.q.y{�A}ljsy��h)g#glh�g�}lu{e�e�u{eUb.}Az�e�nAo�uwejkh)glnly~jsy��h?g³e1b.hKjsywe1n3e�e O jsh)qdq.okb.r�h)glnloUelNÛr àZ�1Ø�rÿ�l��$òrä×A�Ñ� r ¡Z��¢ar £)�ºZ}Abdcfyªcf}A�?osglnAhl��b.oUjs}lz|rlu{o|uweÇy{�)}le?u{n3e1n°���5c.y{u{y~Ã�e?gAnlh�uwe�jkh)glnly~jsy��h)g³nAo�b.}lzUe�r�h)qÁ3u{e?bs�Ajsh)z|rlq.h?�3e?qpuwe�jkh)glnly~jsy��h)g�nlo*h)q.nlokg�rle?qfe�^ÿb.o*q.oknl}ljso�e�j�e?u~js}lu{e?q×)¢ B ¼ ¬ @ ¬ � ¬ ëÍ� ë ¿ @ ¿ r¹×)¢�t�¼ " @ " � "y÷ � ÷ q @ q oP¼ � @ � t�� � " � "y÷ @ ÷ oa� � ÷ � ÷ q @ q v¡vР¬�h)z|h�osbÉnlyªÄÅosq.okg�cfo*nlo�£)�lglh|b.o*jk}lzUrAu{o?���Âe?z|r^hKjsh�bdo%jk}lz|rlu{o�r3e1qfe·��r^h?q.��}lo

à B ¼ ¬ @�"¬ rpà � ×£�¢ � £× " o ¡à � £¡ " o £àO� Ãr&£4 ê3ëÍ `ë¤�©ë ²©e?bÉjsh?glnly{jky{h)gAosbpnlo*h)qdnlosg´£)��¡���×�u{u~ok±1e?g�e?u`bdy{bdc.oszUe�glh�u{y{gAo�e?u¼ � oa¼ q r £

¡ z ¡*¼ q @ q oP¼ � @ " r £¡ z ¡*¼ q @ qq oP¼ � @ q" r £× z ¼ q @ qq oP¼ � @ " @ q r £

Õ  ��}Au~cfy~rlu{y~j�e?gAnlh#uwe��}luªcfy{zUe<okjs}3e?jky��h)g�r�h)q|¡��\qdosbmc��e?glnAh)u{o�uwe'e?g�c.osq.y~h)q�b.oÇu{u~os��e�e¼ � @ " tL@ " x�¡,@ q v�r ¢A�²©e?bÂbdh)u{}Ajsy{h?glosb�¼ � r ¢Z�,@ " r ¢]bdh)g�jkuwe?q.e?zUokg�cfoOy{gljkh)z|r3e1cfy~�lu{okbjkh)g�uwe�jkh)glnly~jsy��h)g�nloxh?q.nlokgÇ��jkh)q.qdosbdr^h)gAnly{okg�c.o*e?u��e1q.��h)u^u~y{glose?uP¡1��¼ � @ " @Äqq r�£)���]b���rl}Aosb�uwe �}Agly{jse�r^h?b.y{�Ay{u{y~n3e?nÇosb³@ " r ¡,@ q ��}lo�b.}Abdcfyªcf}ly~n3e�osg�u{e�b.ok�)}lglnleÇokjs}3e?jky��h)g�´nlyª±Zy~nly{okglnlhÇosg�cfqdo�uwe�rlqdy{z|o�eA�Br^okq.z|y~c.oUnloknl}ljky{q�@ q r £°)¡K�Â�´nlo�e1�K}°�� @ " r £)��Écfy{u~y{Ãse?glnlh|nlo�g�}lok±?h�u{eUrlqdy{z|osq.eU�<u{eUcfokq.jkosqfe�bdo�h)�Acfy~osglo�Á3g3e?u~zUokg�c.o�¼ � r £�°?ÕA�¼ q r £�°{×A� »Âh)q�u{e>r3e?qdc.y{jk}luwe?q�ÄÅh?q.zUe>nlosu�z\�okc.hZnlhÈtÅjsh)g z�}lji¦lh?b�jkosq.h?b�okg bd}cfe?�lu{okq.h�vBuwe�±)okq.yªÁ3j�e?jky��h)g�nlop��}lo5osuAh)q.nlokgUokbOq.o�e1u{z|osg�cfoÈ�*bdo5qdosnl}Ajso5e�u{h)b�bdosgljky{u{u~h)bj°�e?u{jk}lu{h)b¡1��¼ � @ " @ qq r¿ît�¼ q @ ÷q oa¼ � @ q" @ q v�r �It�¼ q @ ÷q oP¼ q @ ÷q oa¼ � @ ÷" v�r�£�¡t�¼ q @ ÷q oa¼ � @ " @ ÷q v�r�£4 ê3ëÍ `ëÍ�°ë Æxo�g�}lo�±)h�b.bdoxb.}lr�h)glnAq3�e?g�jkh)zUrAq.h)�3e1n3e?b�u{e?b:jsh)glnAy{jsy~h)glokb�¦3e?bmcie�h?q.nlokg×A��ºZok�È�}lg�bdo�¦le?�`�� e�±Ky{bmcfh|osgÇ}lg<rlqdh)�lu~oszUe|e1g�c.osqdy{h)qk�3uwe?bpjkh)glnly~jsy{h?glosbÉnlo%h)q.nAosg<�bdh)g

¡1� B ¼ ¬ � ¬o� � � ë�@�ë�r £{z/î B ¼ ¬ @ ¬ � ¬ ë�@�ëIr�£4zÉ� B ¼ ¬ @Ð÷¬ r £4z*£¥¡ B ¼ ¬ � ¬o� @ q� r�£4 à?Õ

Page 65: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

Æxokb.rlqdosjsy{e?glnlh|u{h?b�cZ�okq.z|y{glh)bpg�}lu~h)bs�3rle?qfe�osbmcfo*z\�okcfhKnlh��3e?bmcie�±)okq.y~Álj�e?q¡1��¼ " � "y÷ � ÷ q @ q r £4z î�t�¼ ÷ @ ÷ � ÷ q @ q oa¼ " @ " t�� "y÷ @ ÷ oP� " q @ q v¡v�r £4z�It�¼ q @Ð÷q oP¼ ÷ @Ä÷÷ oP¼ " @Ð÷" v�r�£4z £¥¡Ht�¼ ÷ � ÷ q @ qq oP¼ " t�� "y÷ @ q÷ oP� " q @ qq v¡v�r £4 

�]u`b.}lbmcfy~c.}ly{q�u{h)bpn3eMcfh)bÉnloku°cie?�lu~osqdhl�AcfhKn3e?bpokbdcfe?b]y~�)}3e?u~n3e?nlokbÈb.o%js}AzUrlu~osg°�ê3ëÍ `ëÍ�°ë ²©e�nlosbm±)okg�cfe¥·.e�h)��±Kywe*osbO��}lo5osb:y{z|rluÏ�� jsyªcfhl�©a�ulcie1�lu{okq.h*jsh)g|uwe�glh1cie?jky��h)gnlo*u{e�y{glnly~j�e?jky��h)g�okb ¸ £¥¤1� ¸�x+£�°1�£�x ¸ ×�°M�Vx»¸ £¥¤1�£¥¤)¡ £¥¤)¡

²©e?bvjkh)glnly~jsy~h)glosb�nAoph)q.nlokg�£È��¡�b.oȱ?osqdy~Á3jse?g�cfq.yª±Kywe?u~zUokg�c.o?�B�Ge1z��ly��okg�b.opjk}lzUrAu{osgu{e?bpnlo*h)q.nAosgd×At× B ¼ ¬ @ q¬ rÈ×V� £¡ t�¸ q o¿tУ�x ¸~v q v�r ×

¡ tУex�¡*¸stm£òx»¸�v¡vNr&£Õ B ¼ ¬ � ¬R� @ � r¿× B � ¬o� @ � r¿×�t¡tУòx»¸~vo@ � oP¸�@ q vZr Õ4¸stУ�x ¸~vNr £{ 

²©e?bxnAo�h)q.nlokg'��u{u{o�±1e?g�e�j`�e1u{js}Au{h)bxz��e?b]o�µKcfokglb.h)bk��²©e�jsh)qdq.okb.r�h)glnly~osg�cfo|e?u��e?q.��h)uu~y{glose?uÏ�A¡1� «X¼ ¬ � ¬R� � � ë�@�ë�r £)�lrl}Aosnlo*osbdjsqdy{�ly~q.b.o�zUe1c.q.y{jkywe?u~zUokg�cfo5jsh)z|h|¡1�!\¼ ­LO3O \@�r£)�An3e?glnlh|u{}A��e?qpe� £�¡ £�¡ � ì £°M� ¸�x�£°1�×�°1�}x ¸ £°1� ð ì £°1� ¸�x�£°1�×�°M�(xA¸ £°1� ð ì ¸£ex»¸ ðr � ×Vx»×4¸ ×{¸ � ì Õ4¸�xÊ��¸�q�x+£¡{¸�x>��¸�q1o £ ð  �Écfy{u~y{Ãse?glnlh5e?nlokjs}3e1n3e?z|osg�cfoÈu{e5qdosu{e?jsy��h)gŸÂtm£�xŸ~vNr £°1ÕA�?okuÉ�}luªcfy~zUhp±)okjkc.h)qGjkh)u{}lz��g3eÉosb �÷ � Õ{¸�x+£ à±x\Õ4¸ � ­ �?��}lo8e?u�z�}luªcfy~rlu{y~j�e?q��%e?u�osz|rlu{ose?q©nlo:gK}Aok±)h�uwepq.okuwe?jky��h)ge?g�c.osq.y~h)qs�An3e�osu`q.okb.}luªcie?nAh|okb.r�osq.e?nlhl�²©e�b.ok�)}lgln3e�jkh)glnly~jsy��h?g#nlo�h)qdnlosg°��î*«X¼ ¬ @ ¬ � ¬ ë�@�ë�rÞ£?�°osg�okbdcfo�jse?b.h�bdo�rl}losnAookb.jsqdy{�ly~qpjsh)z|h�� \@ ­ O \@òr £*��}lo�bdo�±)osqdy~Á3jse|jkh)gÇj`�e?u~js}lu~h)bpjsh)z|h�u{h?bÉe?g�cfosqdy{h)qdosb� ¸ £�x ¸ � ì £ ��¸dx�£×Vx>��¸ £ ð ì ¸£�x»¸�ð r8� ¸ £�x»¸ � ì ¡{¸�x+£°{×à4°{×±x�¡{¸�ð r&£4 

²©e�c.osqdjsosq.e�jkh)glnly~jsy��h?g´nAo|h?q.nlokg°�Â� «X¼ ¬ @ ÷¬ r�£)�©os��}lyª±1e?u{o|eÇ¡t�¸ ÷ o ¸ ÷ vVr�£nlh?glnlo ¸"okbposuPjkh)gM·d}l�)e?nlh�q.ose?uPnlo}¸:�O�]g3e�zUe?glokqfe�nAo�jsh)z|rlq.h?�3e?qÈokbdcie�y~�)}3e?u~n3e?nà4ï

Page 66: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

bdy{g"¦le?jsokq�j`�e?u~js}lu~h)b%osb�r�osglb.e?q�okgÊosu:q.okb.}luªcie?nlh<nlo�nlokbfe?qdq.h)u~uwe?q*u~h)b�jk}l��h)b�jsh?g>osu�ly~glh)z|y{h]nloÉ­]o��pcfh)g°��nloknl}ljky{osgAnlh*�K}Ao�¡Ht�¸ ÷ o ¸ ÷ vÂokb:gAosjsokbfe?qdywe?z|osg�c.op}lg�gx�}lzUokq.hokg�c.osqdhl�3jsh)z|h ¸ æ ¢*m î��â¸ æ ¢*m ×Z�3osbdc.o*osg�cfokq.h�nAos��o%bdosq*£)�§Gy~g3e?u{z|osg�c.o?�Au{e+�}lu~c.y{zUe�jsh?glnly{jky��h)g�nlo*h)qdnlosgÇ��u{u~ok±1e�e�u{h)bpj°�e?u{jk}lu{h)b£�¡ B ¼ ¬ � ¬R� @ q� r�£¥¡t�¼ � � �Ì� oP¼ q � q¡� vR@ q � o £¥¡Ht�¼ � � ��q oa¼ q � qÌq vo@ qqr�Õ�tУex»¸�v�¸ q oËÕ4¸Âtm£�x ¸~v q r Õ4¸stУòx»¸~vNr�£

��r�h)qÈcfe?g�cfh�cie?z��ly��okgÇbdo*bfe1c.y{bdÄ e1jso?�ê3ëÍ `ë � ë t ¹�e?y~q.osq�r°�l£à4à{v]��}lgA�K}Ao|¦le��<jsh)gAnly{jky{h)glokb�nlo�h)qdnlosg'y{gZÄÅosq.y~h)q���}lo�glhbdo�bfe1c.y{bdÄ e1jsosgP�`osb�b.okgljsy~u{u~h�jsh)gAb.y{nAosqfe1qxuwe�jkh)glnly~jsy��h)g�nlo�h)qdnlosg\à�jsh?q.q.okb.r�h)glnly~osg�cfoe?u��e?q.��h)u°jkh)g���r¿àZ�

à B ¼ ¬ @ "¬ r¿à � £¥¡4à£�ñ�¡ � ¡ "à " x îA££�ñ)¡ � ¡ "× " £�¢)¢£�ñ�¡ � � "à " � Ãr�£4 

ê3ëÍ `ëÍ °ë ²©eÊjsh)glnAy{jsy��h)g�nlo�h)qdnlosg¹×A�/×*«X¼ ¬ @Ðq¬ r £�n3eÊu{}l��e1q�eÊuwe>okjs}3e?jky��h)gº�qа1�(o�t�×�xPº1v�qÅrØ¡Çjk}A��e?b�qfeA�� jsokb%bdh)g)ºérØ¡��Jºér £���°4àK��a�bdcfe��}luªcfy{zUe�q.el�� Ãy~zUrlu~y{jse?q��� eJ@ ÷ r;ï4°Z£�¢A�[@ " r×£°4àZ�©u{h���}lo|jsh?g�c.qfe?nAy{qs�� e�uwe�jsh?glnly{jky��h)g'nlo�h)qdnlosg³�l�� «X¼ ¬ @ ÷¬ rø£)¸8r^h?q�cie?g�cfhJº r ¡K� @ ÷ r £�°)¡Z�*@ " rø£)�Ê�Écfy{u~y{Ãse?glnlh�h?cfq.e'nAo�uwe?bjkh)glnly~jsy{h?glosbpnlo*h)qdnlosgÇ�î B ¼ ¬ @ ¬ � ¬ ë�@�ë�r¿îV� � Õ � £¡ � £¡ �¸âoPîV� £Õ ��£���t¡tY¡{¸~v�� � � £¡ xétÏ¡{¸�vÚ� � �¸~vNr £{ 

Æxo�nlh)gAnloÛ¸�r £ÇhA¸Ùr £�°1�l����uÉb.}lbmcfyªcf}ly~q·¸�r £Çosupcfe?�lu{okq.h'q.okb.}luªcie?g�c.o�glh±?osq.yªÁ3j�e�uwe�jkh)glnly~jsy��h)g�nlo*h)q.nlokg��A�°£¥¡ « ¼ ¬ � ¬R� @Äq� r&£)�3r^h?qÈcie?g�cfhh¸Jr £�°1�l�ê3ëÍ `ëÍ&°ë �BhZnAh|u~h��K}Ao%¦le����K}Ao�¦3e1jsosqÉbdh)g�u{e?bpb.y~�)}ly~osg�cfokb5jkh)z|rlq.h)�le?jsy~h)glosb

¡1� B ¼ ¬ � ¬o� � � ë�@�ëIr ¡1��t�¼ q � qÌq � qÌq @ q oP¼ ÷ � ÷ q � qÌq @ q vNr�£î B ¼ ¬ @ ¬ � ¬ ë�@�ër¿î�t�¼ q @ q � qÌq @ q oP¼ ÷ @ ÷ � ÷ q @ q vZr&£� B ¼ ¬ @Ð÷¬ rÔ�It�¼ q @Ð÷q oa¼ ÷ @Ä÷÷ vNr�££¥¡ B ¼ ¬ � ¬o� @ q� r £¥¡t�¼ q � qÌq @ qq oP¼ ÷ � ÷ q @ qq vNr £4 

à{î

Page 67: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÌÎÍ ê3ë� °ë ê�+`ë tÏÓxz|y~cfy~nlh�vÑ�ÌÎÍ ê3ë� °ë ê�ê3ë tÏÓxz|y~cfy~nlh�vÑ�ê3ëÍ&`ë ê3ë t ¹�e?y~q.osq�r°�3£à4à4v%­]okjsosb.e?q.y{e?z|osg�cfoâ�6tÏ¡{vhr £)�~�6t�×�vw¦ -�£4zi¡j/��)�6t��4vw¦-�£4zi¡7zÚ×Hzj T j Ðz��·x�£§/��8okg��)okglosq.e?uÏ�˺Zypr3e1qfe�j�e?nleJ�6t��4v�¦3e��v�·x&£�r�h)b.y~�ly{u~y{n3e1nlosbk�¬Èe?qdn¥ª�wOyDr�' yâ 2 q rÙt�zÂx"£�v�{ª�Z��e���}lo]j�e?nleÊ�e?q.��h)u�okc.y{��}lo�cie?nlh�osbdc3�e�nlokc.osqdzUy~g3e?nlhr�h)qpu{h?bȱ?e1u{h)qdosbpnlo*uwe�ÄÅ}Agljsy��h)gâ�6t}�{v��ê3ëÍ&`ë~ö°ë ¹]e�����}lo*q.osrAq.osbdosg�cie1q#�e?qd�^h?u{osbpo�cfy~�K}Aokcie1nlh)bpjsh?g³£)�¼¡Z�H×����|nAo�z�e?gAosqfe��}lo]osuPh?q.nlokg�nlo�u{e?b:okcfy~��}lokcfe?b�qdosb.r�okc.oxuwe1b8nly~q.okjsjsy~h)glokbÈe?bdjsosgAnlosg�cfo�nAo�uwe1b8q.e?z�e1bs�²©e?bÉr�h)b.y~�ly{u~y{n3e?nAosb�bdh)g

&� &q&÷ &"

&� &÷&" &q &� &q

&" &÷ &� &q&÷ &" &� &

q &÷ &" &� &q&÷ &"

Óx��±Zy{e?z|osg�cfo*osu`bdos�)}Aglnlhl�lc.osq.jkosqdh|��jk}3e?qmcfh|q.osrAq.osbdosg�cie1g<}lgÇzUy~b.z|h��e?q.��h)uY�ê3ëÍ&`ë~ü°ë ¬�h?zUh�¬Èe1q.n�ª�wOy±r;t}z}x £�v�{ª�°¦3e���e�u~h�z��e?b0t�z.x £v�{�jsh?glnly{jky{h)gAosbxnloh)qdnlosgdzK��»Âe?qfe#��}lo�}AgÊz\�o�cfhKnlh<bdo�e�nlo�h)qdnlosg»î�nlos��o�bfeMcfy{bmÄ e?jsokq.u{e?b�c.hZn3e1b�jsh?g£}ß�z0ß�îA�O»Bh)qpcie?g�cfh

g � nlo*jkh)gln°��ßÔ¢!{�o £C{oË¡ {o������oãï {�rpà{ñA£�×7 ê3ëÍ&`ë¤�©ë a�±Ky~nlosg�cfokzUokg�cfo�okuÇ�}lgly~jsh �e?q.��h)uOnlo�h?q.nlokg�zÇjsh)g���t���v.rez�osb�oku8��}loc.y{osgAo�c.hZnAh)b�b.}lb�±O�osqdc.y{jkosb|}lgly{nAh)b�nly{qdosjkcfe?z|osg�cfo�jsh?gËu{e'q.el�� Ã1��²Be'jsh?glnly{jky��h)g\nloh)qdnlosgÇb.okq3�e z B ¼ ¬ � � ¬ � ¬ � � ¬ � ¬)(  j j ¡� ¬ � ¬�* r�z B ¼ ¬ @ y � �¬ r�£4z

��oku`nly~ÄÅokq.okgljsy{e?u°osu~osz|osg�cie1uPcfy~osglo�u{e,+ � x��okb.y~z�e�jshKh)qdnlosg3e1n3eI-� � t���v�r B� � Ð/././. Ð � * | ���� � ././. � * |#� � | � (  j j Ú|#� *  ê3ëÍ&`ëÍ�°ë ­5hl�3}lg�jsh)g�c.qfe?oE·dosz|rlu{h�r3e?q.e_z(r¿à�u{h�jsh?gAÄÅh)q.zUe?g�u{h?b��e?q.��h)u~osbst

à{ñ

Page 68: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

&&&& &

& & &&&

��e���}lo%r3e?qfe�e?z��^h)bm��t���vZr ¡?¢A�ê3ëÍ&`ëÍ�°ë t ¹�e?y~q.osqprP�l£à1��ve�vȲ`h)bÉb.y~�)}ly~osg�cfokb<�e1q.��h)u{okbpjs}lz|rlu{okg]�~t O v�rÈ×?¢A�!��tL^0v�r �)¢A�

&¬ & ë & ¿ & �&� & ¬&

� & ¿ & �&ë²`h)bÉnly~ÄÅokq.okgljsy{e?u{okbÈosu~osz|osg�cie?u~osbÉb.h?gI-�Ht O v�r B! Ð jÐ 0GÐ ½ |#�! |1 0 |#0½ | ! | ½ r B! Ð ½ | �! q | qq | q½ | ! | ½I-�t O vNr B! Ð jÐ 0GÐ ½ |#�! | ! 20 |#0½ |3 | ½ r B jÐ ½ | �q | q q | q½ |3 H| ½

Æxh)gAnlo�bdo�¦3e�}lb.e?nlh�r3e?q.e�b.y~zUrAu{y~ÄÅjse?qp��}loh| � r £���r�h)q]cfe?g�cfh�bd}lb�nlosqdy~±1e?n3e1b�b.oe?g�}lu{e?g°��»Bh)q:osbdcfe�z|y{bdz�e�qfe1Ã`�h)glI � t O v�rcI � t}^0v�r ¢A��Æxokbfe?qdq.h)u~uwe?glnAh�uwe?bOb.}Az�e?b��bd}lbdc.y~c.}A�)okglnlhâ|ü��r&£)� |]qÂr5uI q t O vNr�I q tL^0v�r�u � u ��q t�u � ovu q uHvuovu q u qÌq u�t�u � odu q uvР�IvɺZ}lrA}losbmcie?b]uwe?bpjkh)glnly~jsy{h?glosbɦ3e?bmcie|h)q.nlokg��A�3osu©z\�o�cfhKnlh�b.okq3�e�nlo�h?q.nlokg�à�b.y��bl�h)u{h�bdy B­�� Ë54 � £�x���tL��v B ¬ ¼ ¬ $ ¬ tL��v � I6�t���vNr ¢H 

ºZyBuweUjsh)glnAy{jsy��h)g<nAo�h)q.nAosg\àUbdo�js}lz|rlu~o�r3e?q.eUcfhKnlh)b�u{h)b<�e?q.��h)u~osb�nAy~ÄÅosqdosg�cfokb�nlo O�a^`tÅ��nAo�bd}lb]ok��}ly~±1e?u~osg�cfokbÚv���jkh)zUhI?t O vDr�I?tL^�v��3osu©z\�okc.hZnlh�bdosq3�e|nlo*h)q.nAosg�àÕ)¢

Page 69: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

bdy{osz|rlqdo��K}Ao �f£�x»×)¢ B ¬ ¼ ¬ $ ¬ t O v � o �f£ex"��¢ B ¬ ¼ ¬ $ ¬ t}^0v � r ¢H � osbmcie%y{�)}3e1u{n3e?n�rA}losnlo]n3e?qdb.o5js}3e?gAnlhÅ×?¢ « ¬ ¼ ¬ $ ¬ t O vVÃr�£É����¢*« ¬ ¼ ¬ $ ¬ tL^�v±Ãr £)�a�bÉnlosjky{qk�3uwe?bpjkh)glnly~jsy{h?glosbpnlo*h)qdnlosgÇb.h?g�bd}AÁ3jsy~osg�cfokb]r�osqdhUgAh|bdh)gÇglosjkosbfe1q.ywe1bs�j�v�a�u�c.osh)qdoszUeÊosb�r3e?q.eÊrlq.h)�Au{oszUe?bU�)osglokqfe?u~osb�t okgÔuwe"nlo�Á3gly~jsy��h?g y~gly{jkywe?uÉnloh)qdnlosgUnlo�jkh)glbdy{bdc.osgljkywe%b.o�r�osn°�� e?gUjsy{okqdcfe?b8rAq.h)rly~osn3e1nlosb8r3e?qfe*cfhKnlh rlq.h)�Au{oszUe*b.}AÁA�jky{osg�c.osz|osg�cfo%q.ok�)}luwe1qÚv�¸Ab.y{gÇosz��3e?q.�?hUrl}Aosnlokg<o�µZy~bdcfy~qÉj�e?bdh)bÉr3e?qdc.y{jk}luwe?qdosbÉjsh?g�jse?qm�e?j�cfokq��� bmcfy~j�e?bpokb.r�osjsy{e?u{okbs�

Á ê3ëÍ&`ë � ²©e"Ä1�h)qdz�}luwe³nlo'§�eV�e"nlyVá8q.}lglhʱ?osg`�� e>o�µAe?jkcfe?z|osg�cfo'nlo�oѵArAq.osb.e?q�uwenlokq.yª±?e1n3e�nlo*}lg3e�jsh)z|r�h)b.y~jsy��h?g�jsh)gÇosu`u~osgl�)}le¥·do�nlo*u{h)bÇ�e1q.��h)u{okbs�lr�h)qÈcie1g�c.ht�|87suHv ß �j�ür BÒ � :9 � � �Ò 2 ý Ò �iÐ Ò � Ð/././. Ð Ò<;Lþ

t�| ß â ��7muvnu ß A �L� u ß A � �7 j j ou ß A ; �nlh?glnlo�E��ÂokbÉosu`h)qdnlosgÇnlo}å��Ò�»Ge1qfe·¢�r £%uwe��}lgly~j�e�r^h?b.y{�Ay{u{y~n3e?n�okb]��}loY�.r�£%�wå � b.oseUoku��e1q.��h)u°cfqdy~±Kywe?u~t nlo}lgÇb.h?u{h�±O�osqmcfy{jko�vÑ�3u{h���}lo*jsh)qdq.osbdr^h?glnlo�e

tÇ|87muHv m r�t�| m 7muvnu m  »Ge1qfe0¢dr ¡Z�lbdy �(r�£)�Hå � okb5oku%�e?q.��h)u^nlo*}lg3e�b.h)u{e�e?q.y~bdcfeA¸Z��bdy �(r ¡K�å � �wå qbdh)g<e1z��^h?bposu%�e?qd�^h)u^cfq.yª±Kywe?uY�v²©e�Ä1�h)q.z�}Auwe�e?g�cfokq.y~h)qÈy{z|rlu~y{j�e�osg�cfh)gAjsosb

tÇ|=7muv m m r�t�| m 7suHvnu m m o¿t�| m m 7muvnu m u m  »Ge1qfe�¢�r²×A�vbdy~��r £)�~å � okb�osu��e?q.��h)u:u{y~glo�e?uOnlo�nlh)b�e?qdy{bmcie?bk¸:bdy~��r�¡K�Nå ��¶å q nlok�^okg�b.okq�}lglh�osu��e?q.��h)u`cfqdy~±Kywe?u°�Çh?c.q.hUosu��e?q.��h)u©nlo�}lgle�e?qdy{bdcfe�tÅgÉ�h?cfokb.o���}lo¦3e��Çcfqdosb�ÄÅh)qdz�e1b]nlo�okcfy~��}lokcfe?q�oku��e?qd�^h)u©qdosb.}Au~cie1g�c.o�vѸ°��bdy �·r�×A��å � å q �då ÷ b.h?g�e?qd�^h?u{osbÈc.q.yª±Zy{e?u{okbs�GaObmcfh|jsh)qdq.h)��h)q.e�u{e�Ä1�h)q.z�}luwe

tÇ|=7suHv m m m r�t�| m 7suHvnu m m m oP×tÇ| m m 7muHv:u m u m m o¿tÇ| m m m 7muvnu m u m u m  ê3ëÍ&`ëÍ °ë t ¹�e?y~q.osqprP�l£à1��v

ÕA£

Page 70: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

e�vG�]uAcfh)zUe?qÂuÒ�� z|y~c.osb���¾ ¢*bdoph)�Ac.y{osgAopy{glz|osnly{e1cie1zUokg�c.o O � r £?��¬�h)g?Øhr £)�£Do O q ��rÙtm£�x)�]v � � oPÆ¥tL� q vÈy~zUrlu~y{jse O q r £)�O»Âe?qfe?Øhr ¡£]o��so O ÷ � q rÙtm£�x¥�]vÚ� � tУ�x¥� q vÚ� � rÙtУ�oâ�òoâ� q vTtУ�oâ� q v�odÆ¥tL�I÷Ðv>� O ÷ r ¡7 �]b��� bdo�rAq.hKjsosnAo�y~glnl}lj�cfyª±?e1zUokg�c.o>osg&�)okglosq.e?uÏ��nlosb.e?q.qdh)u{u{e?glnlh�tУwx �]v �j�V� tm£wx�IqÄv �j� � ������tУ}x�� � v �j�!� �³�l}lbdj�e?glnAh�osu�jkhZo�Á3jsy~osg�cfo�nAo��)qfe1nlhJØ"��}lo�bdosq3�e OM� � � �a�uxj°�e?u{jk}lu{h>z��e?bUuwe?qd�)h>jsh?q.q.okb.r�h)glnlo'g3eMcf}lq.e?u{z|osg�cfo<e OG� �+okbdc3�e\�le?bfe?nAhÊosgÔosunlokbfe?qdq.h)u~u{htm£�xA�]vÚ� � tУòxA� q vÚ� � tУ�xA�I÷ÄvÚ� q tУex���"6vÚ�¢"#tУexA� � v�� Ü r�tm£Do»�0o»� q o»�I÷�o»��"o»� � v��ntУDo»�·o ��"ÄvTtУDo�¡#�I÷Äv6tm£Do��{��"ÐvTtm£Doañ*� � vüoPÆ¥tL� � vРa�uOjshKokÁ3jky{okg�c.osb�nlo?� � okg"okbdcfoUrlq.hKnl}lj�cfh�b.o�u~hZjse?u{y~Ã�e�Ä1�e?jky{u~zUokg�c.o�}Acfy~u{y~Ã�e?glnAhÇ��}lou{e?b��}lgly{jse?b�ÄÅh)q.zUe?bOnlo5osbdjsq.y~�ly{qDà�jsh)z|h*b.}lzUe�nAo]u~h)b�o�µZr�h)glosg�c.osbÈ��}lo�e?r3e?qdosjsokg�okgokbdcfh?b5rle?qK�okg�c.osbdy{bÉb.h)g´tO¢�oË¢�o\¢�o\¢/oaàZ�°£Zo\¢eo�¢�oÊ�/o�¢Z��¡òo�¢eo»×�o�¢�o�¢A�¢3o�¡3o�×±o+¢/o+¢A�v£Âo��Vo+¢3o+¢±o+¢A��×±o�¡/o+¢±o+¢±o+¢|��à/o+¢±o+¢±o+¢3o+¢A�²`hKj�e?u~y{Ã�e1glnlh�u~h)b�jsh)qdq.okb.r�h)glnly~osg�cfokb�rlqdhZnA}ljkc.h)b*nlo�jshKokÁ3jky{osg�c.osb%b.o�h)�Ac.y{osgAo OG� rñeo��/oË¡eoË¡òo £Do £DoÔ£±r ¡?¢A��Ivv»Âe?qfe���}loÉb.ose*nAoph)q.nlokghî*nAos��o5b.e1cfy~bdÄ e?jkosqvu{e?bvjkh)glnly~jsy{h?glosb�nloph?q.nlokgz�r3e?qfe£.ßcz·ß¹îA�3��b.ok�È�}lg�okuBe?r3e?qmcie?nlhUe?g�cfokq.y~h)qɦ3e���}lg�c.h?cie?u`nAoU£Do £Do+¡�oË�3oPñ/o¡?¢�o\��îeo £)£�à(r ¡?¢)¢�jsh)gAnly{jky{h)glokbpnlo*h)q.nAosg°�

�4� ê3ëÍ&°ëÍ& ��uG�K}Ay~cie1qxuwe�q.el�� Ã�e�}lg �e?q.��h)uGnAo�h)q.nlokg�Ø�o £��K}Aosn3e�}lg «d��h)b.��}lok¯nlo>�e?q.��h)u~osbÅt ��}lo�bdo�b.}Ar^h)gAosg�jsh?g#qfeA�� Ã�vÑ��ºKo�el���Ï�G£0ß�DÂß Ø^�PokuÂg��}AzUokq.h|nlo�osbmcfh)b�e?qd�^h?u{osbp��}lo*bdh)g�nAo%h?q.nlokg�Dd�8Æxok�^o*jk}lzUrAu{y{qdb.o£�� � o�¡§� q oa×,� ÷ o¹������oPØ � � r �B � 2 � �p�ur¿Ø] 

a�uPg��}AzUokq.h�nAoxÄÅh)q.zUe?b�nAoxosu~os�)y~q � � z�� q zj j T 6z�� � ��}lo�js}AzUrlu{e?g�okbdcie�y~�)}3e?u~n3e?n|±Zy~osglon3e1nlh�r^h)qpoku`jshKokÁ3jky{okg�c.o�nAo}� � okgtm£Zo»� �@? � o»� �@? q o»� �@? ÷  j j �vTtУÂo � q�? � o»� q�? q o»� q�? ÷  j j Úv������Ttm£Do � � ? � o»� � ? q  j j �vr�tУ�x)�]vÚ� � tУex�� q vÚ� � ������tУexA� � vÚ� �  ºZy~g<okz��3e?qd�)h�e?u©osu~os�)y~q]u~h)bH���voku��e?qd�^h)u©y~gly{jkywe?u`glh�osbdc3�e�cfh?cfe?u{z|osg�c.o%nAokcfokq.z|y{g3e1nlhl��)e���}lox¦3e�� O �°r�h)bdy{�lu~osbOcfy{r�h)b8nly{bmcfy{g�c.h)b8nAo��e?qd�^h)u~osb8nlo�h)qdnlosg]Dd��²`uwe?zUe?glnAh�E�� ¬ e?ug��}lz|osqdhUnAo�u{h?bH�p���e?qd�^h)u~osbÉnlo�h)q.nlokg D���}lo�b.h)g<nlosu©cfy~r^h�N3�B£0ß�N¶ß O �ϸPb.o%cfy~osglo

Õ�¡

Page 71: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

��}lo�osu�g��}AzUokq.h�cfh1cie?uvnAo��e1q.��h)u{okb�nlo�h)q.nlokg�Ø0o�£�okb�okuvgx�}lz|osq.h�nAo|r�h)bdy{�lu~osbYE�� ¬cfe?u{okbp�K}Ao �B � 2 � D�tiE�� � o�E�� q o¹�����jo�E�� �BA vNr¿Ø] »�q.hKjsoknly{okglnlh�jkh)z|h�e?g�cfokbs�lbdo�cfy~osglo]��}loxosu�g��}lz|osqdh�nloxr�h)bdy{�lu~osb:osu{okjsjky{h)glokbÈnlo]u{h)bE�� ¬ okbÉosu`jshKokÁljsy{okg�cfo%nloV� � osg)t¡tm£�xA�]v � ��v ��� t¡tУex��IqÄv � �¡v � � ������t�tm£òxA� � v � ��v �!� �

ÌÎÍ ê3ë�&°ë ê�+`ë tÏÓxz|y~cfy~nlh�vÑ�ê3ë ên+`ë ê3ë »Ge1qfe�osu%�e?qd�^h)uPu{y{gAo�e?u^uwe�jsh?glnly{jky��h)g�nlo*h)qdnlosg´£�¢�jsh?q.q.okb.r�h)glnly~osg�cfo*okb

£3r�£�¢ {�¼ � � ÜC � 2 � �C��� � ��ß&£�¢!{�t zUeMµÅ� �C��� � �¡� v Ü  Æxokb.r�oз.e?glnAhUbdo%h?�Acfy~osglo�oku`q.osbd}lu~cfe?nlh|�l}lbdj�e?nlhA�

ê3ë ên+`ë~ö°ë ¹�e���¬Èe?q.n�wV�Ojsh?glnly{jky{h)gAosb�nlo�h)qdnlosg Dd�°�#r3e?q.e��K}Ao�}lg'z\�o�cfhKnlh�b.osenlo�h?q.nlokgÝz�nlos��o�bfe1c.y{bmÄ e?jsokq.uwe1b�cfhKn3e?b�jkh)gÊ£wß©D3ß©zZ��»Âh)qxcfe?g�cfh�osuvg��}AzUokq.h�nlookjs}3e?jky{h)gAosbs�EDKy��lokbD � r�£4zFD q r ¡7zFD ÷ rÔ�zFD " rÈîHzFD � r�£�ï7zFD � r¿×�ï7zFD � r¹î�à7zFD � r ¡1¢)¢H ²©e?bxy~glj`�h?�)gly~cfe?b�bdh)g�cfhKnlh)bxu~h)bxoku{osz|osg�c.h)b}�C� ¬ ��D/À5N3�°��u{h)bV¼��OnlokuGcie1�lu{okq.hl�%a�bdc.hokbs�3¦3e�� � A r�tm£ZoË¡eoa×eo¹�����oÈtiEex�£v¡vüo�E±r E�tiEDo £v

¡y~glj`�h)�?gly~cfe?bs�8ºZokq��� e�nlo%osbdr^okqfe?q5��}lo�oѵAy~bdc.y{osq.e?g�cie?�lu~osqdh)bp��}lo�±?osq.yªÁ3j�e1b.osg<uwe?bpokjs}3eM�jky{h)glokbÈb.y^osu^gx�}lzUokq.h�nloxy{gAj`�h)�)gAy~cie1bD� A ÄÅ}lokqfe�zUe��)h)q8h�y{�)}3e1u���}lo�okuPnlo�osjs}le?jsy~h)glosbDKys�O²`h)bp±1e?u{h?q.osbpz��� gAy{z|h)b�nlo�E*r3e?qfe���}lo*b.o%js}lz|rlu{e�osbdcfe|qdosu{e?jsy��h)g�b.h)gz(r�£HG¾ E±r�£?t�D � r&£4z�� � r £v z}rpàIG¾ E3r Õ¶t�D � r £ï7z�� � r ¡K£vz(r ¡JG¾ E±r ¡�t�D q r&£4z�� q r¿×�v z}r ÕJG¾ E3r¿ñ¶t�D � r¿×�ï7z�� Ü r ��à4vz(rÈ×-G¾ E±rÈ׶t�D ÷ r&£4z�� ÷ r Õ�v zVrpïIG¾ E3r�£�׶t�D � r¿î4à7zò� � ÷ rÈñA£vz}r �-G¾ E/r �dt�D " r�£4z�� " r £�¢�v z(r¹î6G¾ E3r ¡1¢dtKD � r ¡?¢?¢Hzò� q �sr ¡Z£�¢4v�]}lgl��}loÇosbdc.h³okb�jsh)¦lokq.okg�c.o�jkh)g�u{h���}lo�e?b.ok�)}lqfe'uwe#�le?q.qdosqfe�nlo¶á�}Aq.ji¦lokqUokgËbd}ÄÅh)qdz�e�z��e?b]bdy{z|rlu{o1t8rle?qfelE·À ��glhU¦3e��Çz\�o�cfhKnlh)b5nlo�h)qdnlosg¥E�� E�o�cie?r3e1bs¸�glh�osb}lgle�rlq.}lok�3e�glyÂb.y{��}ly~osq.e�osg�okbdcfh?bxj�e?bdh)b�r3e?qmcfy~js}lu{e?q.okbs¸^�)e���}lo�osg�}lg�bdy{bmcfoszUe�nlo

Õ4×

Page 72: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

okjs}3e?jky{h)gAosb}tÅglh�u{y~glo�e1u�okg�osbmcfo�j�e1b.h�vÑ�A��}loxokuPg��}lz|osqdh�nloxokjs}3e1jsy{h?glosbpbdo�e�zUe��?h)q�hz|osglh?qÂ��}loÈokuAnlo�y{glj°�h)�)glyªcie?b©glh�e1b.os�?}lqfexu{e]o�µZy~bdcfokgljsy{e�hxy~glo�µZy{bmcfokgljsy{e]nloÈbdh)u{}Ajsy��h?g°�ê3ë ên+`ë~ü°ë ²©e�jsh?glnly{jky��h)g�nAo�h)q.nlokg�jsh)qdq.osbdr^h?glnly{okg�cfo%e?u��e1q.��h)uPu~y{glose?uPnlo�h?q.nlokgÛàokb £�¡?¢�t�¼ � � � " � "y÷ � ÷ q � q¡� oa¼ � � � " � "y÷ � ÷ q � q¡� vZr&£4 

ºZy~g�z+�e?bp��}lo*b.e?j�e?qpÄ e?j�cfh)qpjkh)z �}Agd� "y÷ � ÷ q � q¡� �3b.o*h)�Zcfy{okglo*osu`qdosb.}Au~cie1nlh�nlosbdo�e?nlhA�ê3ë ên+`ë¤�©ë ²©e?bxjkh)glnly~jsy~h)glosb]nlo�h)qdnlosg�y~zUr�h)glokg#��}lo�jsy~osqmcie?b5ÄÅ}lgljsy~h)glokbxr^h?u{y{gp�h1�z|y{jse?b�nlo�jkhZo�Á3jsy~osg�cfokb�okg�cfosqdh)b�ok±1e?u~}3e?n3e1b�osg'u{h)b�osu{okzUokg�cfh)b�nlokuGcie1�lu{okq.h�bdo�e?g�£)�a�bdc.h�y~zUrlu~y{jse���}lo�u~h)bOnlosglh?zUy~g3e?nlh)qdosbOb.y~osz|rlq.oÉbdo]nlok�^okg�b.y~zUrAu{y~Álj�e?qk�)u{h*��}lo�bd}l�1�y~osq.o���}lo:nlok�^okg�e?rle?q.okjsosq©okg%±1e?qdywe?b°ÄÅq.e?jsjky{h)glokbs�G� �e?b©jsh?gljsqdokcie1zUokg�c.o?�1uwepjsh)gAnly{jky��h)gnlo�h)qdnlosgË£Uokbż � o�¼ q op j j �¼ A r�£��'b.yZ¼��:ÄÅ}AosqfeÇ}lg3e�ÄÅqfe?jkjsy��h)g'y{q.qdosnl}Ajsy{�Au{o�jsh?gnlokglh)z|y{g3e1nlh)q|¨ jsh?rlq.y~zUh�jkh)g'u{h)b�nlo�oku�q.osbmcfhÇnlo�u{h)b±¼ ¬ �©osg�cfh?gljsokb�e?uGq.osnA}ljsy~q�ejkh)z �}lgÊnAosglh)z|y{gle?nlh)q�bdoÇu~u{ok��e?qs�� e#e�}lg3e'jsh)g�c.qfe?nly~jsjky��h)gÈt okupnlosgAh)zUy~g3e?nlh?q�b.okq��� ez �}lu~c.y{rlu~h�nloY¨Ø��oku`gK}AzUokqfe?nlh?q5gAh�v��ê3ë ên+`ëÍ�°ë ²©e?bPjsh)glnAy{jsy~h)glokb`nlo�h)q.nAosg*jsh)qdq.okb.r�h)glnly~osg�cfokbGeÈu~h)b*�e?qd�^h)u~osb°jkh)g|��tL��v�rz�t cfhKnlh)bpu~h)bȱO�osqdc.y{jkosb5}lgly{nAh)bÉe|u{e�qfeA�� Ã�v�bdh)gz(r&£�x]¾ B ¼ ¬ r�£z(r ¡äx]¾ B ¼ ¬ @ ¬ r�£°)¡ j j   j j T T j   j T z(rcE�x]¾ B ¼ ¬ @ A � �¬ r £�°CE

Æ�e?nAh)bOu{h)b*@ ¬ nly{bmcfy{g�c.h)bs��osu�bdy{bdc.oszUe%okb8jkh)z|r3e1cfy~�lu{opnAokcfokq.z|y{g3e1nlh*r^h)qd��}lo]oku�nlokc.osqm�z|y{g3e1g�c.oÉnlo]u{e�z�e1c.q.y~Ãpnlo�jkhZo�Á3jsy~osg�cfokb�osb:osu�nlo5¶:e?glnlokq.z|h)glnlo ' �ML ¬ t}@ ¬ x�@��Lv±Ãr ¢A�ê3ë ê�ê3ë ê3ë e�v%²©e?b�jkh)glnly~jsy{h?glosb�nlo�h)qdnlosg+£U�Ê¡Z��« ¼ ¬ r £?�O¡�«í¼ ¬ @ ¬ r £)�vb.o±?osq.yªÁ3j�e1g°�3zUy~osg�cfq.e?bp��}lo.× « ¼ ¬ @ q¬ r�£)�3��}lo*okb]nlo*h)qdnlosgd×A�lgAh|bdo�jk}lz|rlu{o1��Iv5»Ge?q.e�cfhKnlh��e?qd�^h?u��Énly~bdc.y{g�cfhUnlosuÂu{y{gAo�e?uY�3osuGnAy~ÄÅosqdosgljkywe?u©oku{osz|osg�cfe?u I � t���v5b.oe?g�}lu{e|r�h)qd�K}Ao�bdy¦3e��Çe?u~�)}lg3e�qfe1zUyªÁ3j�e?jky��h)g�n3e1q3�e�u{}l��e1q]e�Ä e?j�cfh)qdosb�jkh)g<nAosq.yª±1e?n3e?bbdos�)}lgAn3e?b�nlo�|Â��a�gÔuwe"Ä1�h?q.z�}lu{e"r3e?q.e>osu�nlokbfe?qdq.h)u~u{h>nAosu�osqdq.h)q�nlo�cfq.}Aglj�e?jky��h)gtÅjsh)g Ê r ¡4v���osu�nlyªÄÅosqdosgljkywe?uloku{okzUokg�cfe?u�nlosu]�e?qd�^h?u3u{y{gAo�e?u3e1r3e?q.okjso5z�}luªcfy{rAu{y{jse?nlhxr�h)q£Ix�Õ « ¼ ¬ � ¬R� @ � ��}loÈrle?qfe�okbdc.oÈz\�o�cfhKnlh�bdope?g�}lu{eA�Â�]b��� rl}losbk�¢¯ � r ¢ü��¯q � �To?Æ¥tǯ " v��oku`z\�o�cfhKnlh�osb5nlo*h)qdnlosgd×�r3e?qfe�okbdcfh?b]rlqdh)�lu~oszUe?bÈu{y~glo�e1u{osbk�

Õ?�

Page 73: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ê3ë ê�ê3ë~ö°ë ¬�h)z|hUbdo�¦3e?�°�� e�±Ky{bdc.hl�3cfhKnlh)bÉu{h?b5nAy~ÄÅosqdosgljkywe?u~osbÉosu~osz|osg�cie1u{osbÉoѵAjkosrAc.hoku�jsh)qdq.osbdr^h?glnly{okg�cfo³e?u´�e?q.��h)u�u~y{glose?u�bdo"e?g�}lu{e?g°� a�g oku�j�e?bdh�nlo'h)qdnlosg �ËokbdcfonlyªÄÅosqdosgljkywe?u°bdosql�eI-�}r B! Ð jÐ 0 | �! | ! |3 0 |#0�r B � Ð ë Ð â � ¬o� � � ë��]ëàâ B A �gâ A l A  a�bdc.h�jsh?y{gljky{nlo�jsh)g#u{eN+)rcN?�?�osb.y~z�e�jshKh)qdnlosg3e1n3e�nlo�� �,� �,� �C�Èl��x»Bh)q�h1cfqfer3e1qdcfo�okbÈÄ1�e?jsy~uPjkh)zUrAq.h)�3e1q���}lo�cfhKn3e?bÈu{e?bÈzUe1cfqdy{jkosbÈnloku°osgAos}lgljkywe?nAh|jk}lz|rlu{okgÇ��}lo� " okbxuwe|z�eMcfq.y~Ã�g�}lu{eA���]b��� ��}lo�b.o�c.y{okglo�jkh)zUh�e?g�cfokb|¯ � r�¢}�{¯ ÷ � ��o�Æwt�¯ � vÉ�oku`z\�o�cfhKnlh�osb5nlo*h)q.nAosgÇ�|rle?qfe�osbmcfo%rlq.h?�lu{okz�eA�a�bdc.h�glhÇjsh?g�c.qfe?nAy{jso�okuvcfosh?q.oszUe�zUokgljsy~h)g3e?nAhÇr�h)qd�K}Ao|oku�h)q.nAosg´��okb%bl�h)u{h�okgjse?b.h)bÉokb.r�osjsy{e?u{okbs�:a�g��?osglokqfe?u`okb5bl�h)u{hU¡Z�

�4� ê3ë ê�ê3ë{ü ¬�h)glbdy{n8�okq.okglb.o�nlh?b��e?qd�^h)u~osb]nlo�h)qdnlosg#�Ucie?u~osb���}lo�rle?qfe�rAq.h)�lu~oszUe?bokb.j�e1uwe?qdosbÉu{h)bpnAy~ÄÅosqdosgljkywe?u~osbÈoku{okzUokg�cfe?u{okbpglh|b.o�e1g�y~glnlosr�osgAnly{okg�c.osbk��»Bh)qÉoзdosz|rlu~h

&&O r & &

& & &&^Ùrjk}lzUrAu{osgaI?t O vNrcI?tL^0v�rÈ| m m¤|Imè|]q��O»Âe?qfe�qdosb.h?u~±)okqposu^rlq.h)�Au{oszUe��3e1bdcie�okgljsh?g�c.qfe?q}lg�zÊ�okc.hZnAhxnloÈh)qdnlosg·×x��}lo�bfe1c.y{bdÄ e1��e�uwe1bGjsh?glnly{jky{h)gAosbvnlo�h)q.nlokg���jsh)qdq.okb.r�h)glnly~osgZ�c.osb5e�cfhKnlh)bÉu{h)bÇ�e1q.��h)u{okbpnly{bmcfy{g�c.h)bpnlo O �a^��3��}lo%glh�uwe?bpjk}lz|rluwe�r3e1qfe O �a^�¸l���}lo*b.y~g�okz��3e?qd�)h� £òx���t O v B ¬ ¼ ¬ $ ¬ t O v � o � £�x���tL^�v B ¬ ¼ ¬ $ ¬ tL^�v � r ¢H ¬�h)g�oku{u{h�b.o%e?b.ok�)}lq.e���}lo*oku°nlosb.e?q.qdh)u{u~h�nlosuPosq.qdh)qpnloxc.q.}lgljse?jsy��h)g�r3e?q.e�rAq.h)�lu~oszUe?bokb.j�e1uwe?qdosb`b.oseM¯ � r ¢�¤¯ ÷ � �¡o}Æwtǯ � v��¥zUy~osg�cfq.e?b°��}loOjsh?zUhÉglhpcfhKn3e?bPuwe?b`jkh)glnly~jsy{h?glosbnloÇh)qdnlosg+�³b.o�js}lz|rlu{okg°��bdos���}lgËosuÉcfokh)q.okz�e'nlo�á8}Acfji¦lokqs�pbl�h)u{h´b.oÇcfy{okglo�¯ � rÆ¥tǯ ÷ � ��v8��glhJ¯ � r¹Æwtǯ " � ��vÑ�»Ge1qfeÊjsh)gAb.os�?}ly{q�}lgÔz\�okc.hZnlhÊ��}lo'b.e1cfy~bdÄ e?��e>z�}lji¦3e?b�jkh)glnly~jsy{h?glosb�nlo�h?q.nlokg¦3e1bdcie�h)qdnlosg\�l�Ookb�jsh)g�±)okgly{okg�cfoÇosb.jkh)�)okq|u~h)b0¼ ¬ ��@ ¬ nlo�e?u{���}Ag>z\�o�cfhKnlh#nlo�okbdcfoh)qdnlosg)t jkh)gÇosu{u~h)bÈbdo*c.osglnAq3�e|e?}Acfh?z+�e1c.y{jse?zUokg�cfoO$,« ¼ ¬ @ ë � �¬ r £v��O»Bh)qÉoзdokzUrlu~h

Õ�à

Page 74: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

¢£¥¤{× £¥¤{×£¥¤{× � ÷ � � ÷ q£¥¤)¡ � " � � " q � "y÷£ � � � � � q � � ÷ � � "£¥¤?Õ ¢ ¢ ¡?¤{× £¥¤1Õ²©e?b�jkh)glnly~jsy~h)glosb%nlo�h?q.nlokg+£U�"¡�bdo�js}AzUrlu~osgÊe1}Acfh)z��e1c.y{j�e1zUokg�c.o?�Be?bs�� jkh)zUhu{e?b*nlo�h)q.nlokgA×��'��jkh)q.qdosbdr^h)gAnly{okg�c.o�e#e�u{h?b"�e1q.��h)u{okb�jsh)gÝ�~t���v}rä×Ç���~t���v}r �l�qdosb.r�osj�cfyª±?e1zUokg�c.o?�:§�e?u~cfe?g�y~zUr�h)glokq�uwe1bpnlo�h)q.nAosg¶×�����r3e?q.e�u~h)b��e?qd�^h?u{osb�u{y{gAo�e?u~osbe?bs�� jsh?zUh�uwe�qdosu{e?jsy��h)g�e?g�cfokb5z|osgAjsy{h?g3e?n3e�okg�c.q.o*uwe1bpjsh)glnAy{jsy~h)glokbÉe?b.hKjsy{e?n3e?bÉe O �^��Oa�b5nlosjky{qk�

Õ B ¼ ¬ � ¬R� @ � r&£ ¡1� B ¼ ¬ � ¬R� � � ë�@�ë�r�££¥¡ B ¼ ¬ � ¬R� @ q� oPî B ¼ ¬ @ ¬ � ¬o� @ � r £

�]nlosz��e?bɦ3e�����}lo*y{z|r^h?glosqÈu{e?bpjsh?glnly{jky{h)gAosbÉnlo*b.}lzUe�r^h?qÈÁ3uwe� ÷ � oP� ÷ q r £× z � " � oP� " q oa� "y÷ r £

¡ z � � � oa� � q oP� � ÷ oP� � " r&£4 a�bdc.h�¦3e1jsosg�Õ�osjk}3e?jky{h)glokb�jkh)gâñ�y~glj`�h?�)gly~cfe?bs��e1b��� �K}Ao�osb8nlo�okb.r�osq.e?q���}lo]r^hKn3e?z|h)boku{os�?y{q�c.q.osb%nlo>�osbmcie?b%jsh?zUh�r3e?ql�e?z|okcfqdh)bs�|ºKo�e?g´r^h?q%oE·dosz|rlu{h�� ÷ q r=� "y÷ r=� � " r£)� a�bdc.h>y{z|rlu{y~j�eat nAo�� ÷ � o � ÷ q r £�°{×�v��K}Ao�� ÷ � r x�¡4°{×A� ºZ}lbmcfy~c.}A�)okglnlhÊokgu{e?b�osjs}le?jsy~h)glosb�e?g�cfokq.y{h?q.osbUb.o�h)�Acfy~osgloÇ}lgËb.y{bmcfokz�e´u{y{gAo�e?upnloÛà´okjs}3e1jsy{h?glosb|��ày~glj`�h)�?gly~cfe?b

�It�� " q o £�vüo¿t�� � q oP� � ÷ v�r ס � " � oP� " q o £3r £

¡×�¡t�� " q oÔ£vüo £¥¡Ht�� � q oP� � ÷ v�r�£à � � � oP� � q oP� � ÷ oÔ£±r&£�It�� " q o £�vüo £�Õeo��4� � ÷ r¿×

��u`qdosb.h?u~±)okq.u~h|bdo*u{u{ok��e�e?uPcfe?�lu~osq.h¢£¥¤{× £¥¤{×£¥¤{× xx¡{°{× ££¥¤)¡ x3×�°K£�Õ x3à4°Z£�Õ ££ à4°1� �4×�°Z£�Õ x�Õ{×�°Z£�Õ ££¥¤?Õ ¢ ¢ ¡)¤{× £�¤?Õ

Õ)Õ

Page 75: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÌÎÍ ê3ëYê�ê3ë¤�©ë tÏÓxz|y~cfy~nlh�vÑ�ê3ë êZö°ë ê3ë ¬�h)glb.y~nlosq.e?glnlhUosu©nlokbfe?qdq.h)u~u{h|nlo��Âe��Ku{h)q5nloY� > osg�¯dr ¢Z�^jse?n3eUjkhZh?qm�nlokg3e?n3e�nlosu:osqdq.h)q.lut�¼6vZx�� > b.okq3�e#nloUuwe�ÄÅh)q.zUeÛ�.¯4É/oÈÆwt�¯4É � �yv¥tÅr^h)q%nlo�Á3gly{jky��h)gnlo�h)q.nlokg�nlo�jkh)g�±)osqd�)osgAjsywe4v5�<u~h�z|y{bdzUhUr3e?qfe?lut�¼6vNxv� qn> j�e?z��lywe?gAnlhâ¯�r^h?q�¡4¯°�®Éosbmcie?glnAhUbdo%h?�Acfy~osgloX�� qn> xd� > X�r�ø»tÏ¡ É x�£v¡¯ É oPÆ¥tǯ É � � vÄz ø Ãr ¢7 

¬Èe?z��lywe?gAnlh�nlo*g�}lok±?h�¯Çr�h)q5¡4¯Ç��nly~±Ky{nAy{osgAnlh�uwe?bpy~�)}3e?u~n3e?nlokbÈjsh?q.q.okb.r�h)glnly~osg�cfokbX�� " > xd� qn> XX�� qn> xd� > X r ¡6ÉÂoPÆwt�¯Iv£DoPÆwt�¯Iv r ¡ É oPÆ¥tǯIvÄ 

�Bh)zUe?glnlh�u{h?��e?q.yªcfz|h)bO��uÒ�� zUyªcfosb8js}3e1glnlh¥¯w¾ ¢�bdo%c.y{osgAo�uwe�Ä1�h)q.z�}luwe�nAosb.ose?n3eA�ê3ë êZö°ë~ö°ë e�v*�Âh)zUe?glnAh�u{h)b%±?e1u{h)qdosb�nAo¶¯\z|osglh?q.osbk��j�e?��o�osbdr^okqfe?q�}lg3e#z|oзdh)qe?rAq.h�µZy{zUe?jsy��h)g°��ºKo%okbdc.y{zUe�okg�cfh)gljkosb5osu`okq.q.h?q5r�h)qu{h?�±� l4½/tY¢#m΢)Õ�¡{à4v1xAl{½3t ¢*m΢4×Z£¥¡4à4v���x>u{h?�}� l4½/tY¢*m ¢4×A£¥¡{à4v1xAl{½3t ¢*m΢A£�à?Õ�¡4à4v��

u~h)�:¡ ¡ ¡7 �IvɺZy`oku`h)q.nlokg�okb]¡Z�lr3e?q.eh¯�r^ok��}lo� glhl{½ Ð > ¡ lut�� ½Âvüoa�ů q z l{½ Ð qn> ¡ l�tL� ½DvüoP�?tÏ¡{¯ v q  

Æxo�nlh?glnlo � l�tL� ½Dv�xAl4½ Ð > � ¡ � �â� ¯ q ¡ � l4½ Ð > xAl{½ Ð qn> �×  �]uvb.}lbmcfyªcf}ly~qxu{h)b]cfq.okb\�}Au~cfy~zUh?b5±1e?u~h)q.okbxnloh¯´bdo�h)�Acfy~osglokg'q.osbdr^okjkc.y~±1e?z|osg�cfo�jkh)zUhokbdcfy~z�e1jsy{h?glosbÈnAosu©osqdq.h)q�×*mΡ4ï±��£�¢ �n÷ �P£Tm ×A£���£�¢ �n÷ �â×*m ×4îV��£�¢ �¢" �

ê3ë êZö°ë~ü°ë ºZys� lut�� ½Dv�x l{½ Ð > � ¡ øJ¯ É ��ø Ãr ¢A¸lb.o�c.y{osgAoÊg¡ u{h)�V� lut�� ½Dv�x l{½ Ð qn> �xÊu~h)�±� l�tL� ½Dv�xAl4½ Ð > �u~h)�8¡  

¬�h)gÛ¯âr ¢*m΢A£à?Õ�¡{à�b.o%jsh)glbdy{�)}Ao Ê]¡ £Tm ñ�ï1Õ� T j p��}lo�okb]jkh)¦lokq.osg�c.o�jsh?g�u{e|e1g�c.osqdy{h)qokbdcfy~z�e1jsy��h?g Ê r ¡Z�Õ�ï

Page 76: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ê3ë êZö°ë¤�©ë e4v]ÆxosgAh?cie?gAnlh¥l � � �� e�u{e�e?rAq.h�µZy{zUe?jsy��h)g�nAo�a�}lu{okq�osgd� � � �� r � � o¯I°)¡Z�l � � �� r¹l � o ¯

¡ |~t�� � z¡l � vÄz l � � � r¹l � � �� o ¯¡ |~t�� � � �� z�l � � �� vРºZ}Abdcfyªcf}A�?osglnAhl�

l � � � rÈl � o ¯¡ |~t�� � z�l � vüo ¯ ¡ |~tL� � o ¯ ¡ z�l � o ¯

¡ |~tL� � z�l � v�vÄ �IvOºZose(l � � � Ð > uwexÄ1�h)qdz�}luwe]r3e?qfe�oku3z\�o�cfhKnlh*nlo5aO}Au{osqOjkh)g�r3e?b.hů|��bdo�e}l � � � Ð >6��qu{e]Ä1�h)q.z�}luwe5nlosu3e1r3e?qdcfe?nlh�e1g�c.osqdy{h)qk��ºZok�È�}lg�uwe]o�µKcfq.e?r^h?uwe?jky��h)g�nAoò®5y~ji¦3e?qdnlb.h)gP��r3e?qfeÊ r £?t oku`h)q.nAosgÇnlosu`z\�okc.hZnlh�nlo%a�}lu~osqÚv

l � � � Ð >Ä��q o l � � � Ð >Ä��q x l � � � Ð >¡ É x+£okb5}Ag3eUe1rlq.h�µZy{zUe?jsy��h)g�nlo*zUe��)h)qÉh)qdnlosg°�:»Bh)qpcie?g�cfh�oku`z\�o�cfhKnlhl � � � r*¡*l � � � Ð >Ä��q x l � � � Ð >r±l � oã¯I|~tL� � o ¯

¡ z�l � o ¯¡ |~tL� � z�l � v�v

nlok�^o�bdosqÈnAo�h)q.nlokg\tYe?u^zUokglh)b�vÈ¡Z�OÆxo�¦Aosji¦lh|osbÈoku°z\�okcfhKnlh�nAo�a�}lu{okqÈzUhKnlyªÁ3j�e?nAhl�ê3ë êZö°ëÍ�°ë ¬�h?zUhUosg#okuGoзdokq.jky{jsy~h�e?g�c.osq.y~h)qs��b.y�l � � � Ð > jsh?q.q.okb.r�h)glnlo�e�e?rlu~y{j�e1q5}Agz\�okc.hZnlhUnlo�h)qdnlosg Ê }Ag3e�±)okÃ�jsh)g�r3e1b.h¶¯�zUy~osg�cfq.e?b���}lo0l � � � Ð >Ä��q jsh?q.q.okb.r�h)glnlo�ee?rAu{y{jse?q.u~h�nlh?b5jkh)gÇr3e?b.h¥¯I°)¡Z�lokg�cfh)gljkosb

l � � � Ð >Ä��q o l � � � Ð >Ä��q x l � � � Ð >¡ É x+£n3e�u{}A��e?qÉe�}lg<z\�okc.hZnlh�nlo%h)qdnlosgAtYe?u`z|osglh?bÚv Ê oÔ£)��®Òc.osq.e?glnlh|osu©rlqdhZjkosnly~zUy~osg�cfhbdo�jsh)glbdos�)}Ay{qs�� e�}lgAh|nAoxh)q.nAosg Ê oÊ¡K� Ê o�×A�lokc.j?�Oa�g�uwe%rlq3�e?j�cfy~j�e�osbmcfh�glh�rAq.hKnl}ljsoz\�okc.hZnlh%nloxh?q.nlokg�e?u~c.h���}lo]b.ose?g�y{g�cfokq.okbfe?g�cfokbÈr�h)q.��}lo]j�e?��o�okb.r�osqfe1qÈ��}lo�okg�j�e?n3ey~gljsqdosz|osg�cfh�nlo�h)q.nlokg�b.opnl}Arlu{y~�K}AoÈosulg��}AzUokq.h�nAopok±1e?u{}le?jsy~h)glosbÂnloÈÄÅ}lgljky��h)gP�)u{hx��}lon3e�u{}l��e1q8e�}lg�jsqdosjsy~zUy~osg�cfh�o�µZr�h)glosgAjsywe1u^nlokuPg��}lz|osqdh�nlo]okcfe?r3e?bÈokg�jsh?zUr3e1qfe?jky��h)gjkh)g�oku`h)q.nAosg°�

ê3ë êZö°ëÍ�°ë e�vȲ©e?bÉjsh?glnly{jky{h)gAosbpnlo*h)qdnlosg´��¡���×|bdo�±)osqdy~Á3jse?gÇjsh)gÇu{h)bpj°�e?u{jk}lu{h?b£Õ o ¡× o £

Õ r £4z]¡ � £× o £Õ � r £4ze×�� ¡× � £� o £

Õ.� r�£4z5ÕV� £Õ � � × � £¡ o £× vZr&£4 Õ4î

Page 77: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ºZy~g�osz��3e1q.�)hl�Auwe�nlo*h)qdnlosgÇ�Ujkh)q.qdosbdr^h)gAnly{okg�c.o%e?u%�e?q.��h)u

&¬ & ë & ¿&�glh�bdo%±?osq.yªÁ3j�eZt î B ¼ ¬ @ ¬ � ¬ ë�@�ëIr¿î4¼ " t�� " q @ q oP� "y÷ @ ÷ v}Ãr&£4 ¬�h)gÛ¯wr ¢ m ¢4×4ï4àZ�lbdo*c.y{okglo*uwe�e?rlqdh)b.y~z�e1jsy��h?g�r3e?q.e|oku°h)q.nAosgÇosz|r`�� qdy{jsh

u{h)�QP2RSR�T:R�tÏ¡{¯ v�xÊu~h)�UP2RSR�TVRutǯIvu{h)�:¡ r¿× m ñ?��Õò j j 

a�bÉnlosjky{qk�3osu`h)qdnlosg�cfo°�h)q.y~jsh�osb/×���osu`okzUr°�� q.y~jsh��l��Iv�­]h´¦3e��\jsh?g�c.qfe?nAy{jsjky��h)g\okg�osu~u{h�r�h)q.��}loÇosuÉh)qdnlosg�osz|r`�� q.y{jkh�b.oÇj�e?u~js}lu{e?�3e}lb.e?glnlh�nle1cfh)b]nlo�}lg<rlq.h)�Au{oszUeUjkh)gljkq.okc.h�osg�}lg�rA}lg�cfh�n3e1nlhl�^��b.y~g#osz��3e?q.�?h�uwenlo�Á3gly~jsy��h?g>nlo�h)qdnlosg¹t cfo`�h?q.y{jkh�v%qdos��}lokq��� e#okbdc.y{zUe?jsy~h)glosb��K}Ao�b.o�jk}lzUrAu{y{okb.okgÊr3e?qfec.hZnlh�rlqdh)�lu~oszUe�b.}AÁ3jky{okg�c.osz|osg�cfo%q.ok�)}lu{e?qs�ê3ë êZö°ë � ë ºZy1P2RSR�TVRut�¯ v ¡ �.¯4É���� Ãr ¢A��osg�c.h)gljsokb8oku3u{h)�)e?q.yªcfz|h�nloku3osq.qdh)q�osbO}lgleÄÅ}lgAjsy��h?g<u{y~glo�e1u`nlosu©u{h?��e?q.yªcfz|h�nlo0¯<jkh)g#r�osglnAy{osg�c.o Ê �]ºZo%rl}loknlo�¦3e?jkosq]q.os�?q.osbdy��h)gu~y{glose?uljsh?g�u{h?b:u~h)��e?qdy~c.zUh)bÂnlo5u{h)b�±1e?u{h?q.osbOnlo5uwexcfe?�luwe*h%b.y{z|rlu~osz|osg�cfop}lb.e?q:uwe?bOnlh)bjkh)q.qdosb.r�h)glnAy{osg�c.osb]e�u~h)bpz|osglh)qdosbp±1e?u{h?q.osbpnAoů���uwe�Ä1�h)qdz�}lu{e

r^okglnly~osg�cfo3r Ä lÄ � r u{h)�:¢*m ¢)¢?��à{î±x"u{h)�:¢*m ¢)¢4×)Õ4îu~h)�Itm£�°Z£ï4v1x"u{h)�ItУ°Z£�î4v r¹× m îò j j 

��oku`h)q.nlokg�okzUr°�� q.y~jsh�okb5�A�ê3ë êZö°ëÍ °ë ºZyV¯�osb�bd}AÁ3jky{osg�c.osz|osg�cfo'r�os��}lo� glh>�Ëu{h?b�osqdq.h)qdosb�nlo�qdosnlh?glnlosh\glhy~g�c.osqm±Zy~osglokg°�©osu�okq.q.h?q%nAos��oUbdosq*jsh)z|h¶�ů É ���iÃr ¢A�°�'r�h)qxcie?g�c.hÇbd}"bdy{�)glh�nlok�^ojkh)y{gljky{nly~q�bdy{osz|rlqdo%jkh)g�osu`nlo.���ÌÎÍ ê3ëYêKö°ëÍ&°ë tÏÓxz|y~cfy~nlh�vÑ�ÌÎÍ ê3ëYêKö°ë ê�+©ë tÏÓxzUyªcfy~nlh�v��

Õ4ñ

Page 78: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ê3ë êZü°ë ê3ë ºZok�È�}lg�uwe�o�µKcfq.e?r�h)uwe?jky��h)g�nlo(®5y~ji¦3e?q.nAb.h)g°�3u{e�osbmcfy{zUe?jky��h)g�nloku`osqdq.h)qÉosbl q x ¤l q¡ ÷ x�£ ¡ × m �}��£�¢ �n÷  ��uwe�Ä1�h)q.z�}Auwe�nlosuBj�e1z��ly{h|nlo�r3e?b.h�t b.y~g�Ä e?j�cfh)q5nlo�b.os�?}lq.y~n3e?nIvÉb.}l�)y~osqdo%c.h)z�e1q5}Agr3e1b.h|nlo�cie?zUe� glh�e�u{h�z��e?b

¯ m r ¢ m £ � ¡±��£�¢ �n÷× m �}��£�¢ �n÷ � ���Rß ÷ � � � r ¢ m ¢4î�ïs j j ê3ë êZü°ë~ö°ë ²©e�Ä1�h)q.z�}Auwe�r3e?q.e�osu`z\�okcfhKnlh�nlo%a�}lu{okqpjsh)gÇr3e?bdhw¯°�3okg�okbdcfo*jse?b.h|osbl � � � r�tУZoã¯Iv�l � oã¯Éb.osg�t�� � l � vР� uwe1bÉÄ1�h?q.z�}lu{e?bp��}lo�e?rlq.h�µZy{zUe?g�osu©okq.q.h?qÅtÅu{hKj�e?u v:��j�e1z��lywe1g�oku`r3e?b.hUb.h)g�q.okb.r�osj��c.y~±1e?z|osg�cfo ú ¡ l � � q x ¤l � � q¡ � x�£ z ¯ m r ¢ m ñ�¯�W ¢ m ¢Z£ú

nlh?glnlo ¤l � � q okbvosuZq.osbd}lu~cfe?nlhxnAope?rlu~y{j�e1qBokuAz\�okc.hZnlh]nlopa�}lu~osqG}Ag3exb.h)u{e5±?osÃ?�Ke�rle?qdc.y{qnlo?t�� � z�l � v��3r�osq.h�jkh)g�rle?b.h�¡4¯°�Oa�b]nlokjsy~q¤l � � q r�tm£DoË¡4¯Iv�l � o�¡4¯Éb.okg�tL� � l � vÄ »Ge1qdcfy~osglnAhUnloV�I����l*�sr&£�jkh)gd¯wr ¢*m{£)�lbdo�h)�Zcfy{okglo� � r ¢ m £ l � r�£Tm{£� q r ¢ m ¡ l q r £TmΡ)¡?¢4ñò j T  ¤l q r £ m ¡X� ú ¡ ¢ m ¢�¡1¢4ñ

¬�h)z|h|osuBosq.qdh)q�bd}lr�osqfeUosu©cfh)u~osqfe1nlhl�3b.o�nlos��osg#nAosb.jse?qdcfe?q�okbdcfe?bxnlh)b5y~c.osq.e?jsy~h)glosbÉ�qdosr�okcfy~q.u{e?bÈjsh?g�oku`gK}Aok±)hUr3e?bdhw¯HmHr ¢*m΢)Õ�¡Z£� j j p¬�h)g�oku{u~h� � r ¢ m ¢)Õ�¡Z£� j j Èl � r £Tm ¢)Õ�¡Z£� j T � q r ¢ m £¥¡1��¡s j j Èl q r £Tm{£�×�¡)¡s j T  ¤l q r £ m £¥¡1��¡s j T Y� ú ¡ ¢ m ¢)¢�ï{ña�bdc.o]±1e?u~h)q8okbÈe?nAzUy~b.y{�Au{oÈ�|b.o]rl}losnAoxnly{bdzUy~g�}ly{qOosu�r3e1b.h�¦3e1bdcie�¯ m r ¢ m ¢�à4à1Õ� T j :²©h��}lo*n3e�u{}l�)e?qpe� ÷ r ¢ m £�î)Õ4ñò j j Èl ÷ r £TmΡZ£)£¥¡s j j � " r ¢ m ¡1��ñ)Õò j j Èl " r £Tm ×)¢�¡?¢ò j j  ¤l " r�£ m ¡{ñA£ïs j T Z� ú ¡ ¢ m ¢?¢A£�¢4×

ï?¢

Page 79: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

Æxo�g�}lo�±)h�¦3e���nlosbdj�e?qmcie?q�okbdcfh?bÇqdosbd}lu~cfe?nlh)b���qdosr�okc.y{q.u~h)b�jkh)g¿¯ m r ¢ m ¢�à{à?Õò j j Óx�Ac.osgly��osglnlh?b.o� ÷ r ¢ m £ï{ñ4îò j j Èl ÷ r £TmΡ?¢4×)¢ò j T � " r ¢ m ¡{×�à4às j j Èl " r £TmΡ{îA£�îò j T  ¤l " r £ m ¡4ï{×�ïs j T Y� ú ¡ ¢ m ¢)¢4î)¢ºZo�rl}Aosnlo�e?}lz|osg�cie1q|u~y{�)okqfe?z|osg�c.o�osupr3e1b.h´¦3e?bdcfe)¯Hmòr ¢#m΢�à4à{ïò T j �²©e?b��}lu~c.y{zUe?byªcfosq.e?jsy~h)glokbpb.h)g� � r ¢ m ¡{ñA£¥¡s j j Èl � r £ m ×)Õ4ñ4îò j T � � r ¢ m ×?��Õ?�� j j Èl � r £Tm¼��Õ�ï4ïs j T  ¤l � r £ m ��à4ï4ïs j T Y� ú ¡ ¢ m ¢)¢4ñ4ñ

ÌÎÍ ê3ëYêKü°ë~ü°ë tÏÓxz|y~cfy~nlh�vÑ�ê3ë ê��©ë ê3ë ºZok�È�}lg�u{h)bpn3eMcfh)bÉnloku`rlq.h)�Au{oszUeA�Zosu°cie1�lu{okq.h�osb

¢ ¢ ¢ ¢£¥¤)¡ £¥¤)¡ ¢ ¢£ ¢ ¢ £¢ £ ¢£°?Õ ¡{°{× £�°?Õa�u�rlq.y~zUokqOz\�o�cfhKnlh�okb�nlo]h)q.nAosg�¡ht u{e?b8jkh)glnly~jsy~h)glosb:nlo5h)q.nAosg�bdo�js}AzUrlu~osg|cfq.yª±Kywe?u �z|osg�cfojv8��oѵArAuÒ�� jky~c.h���e���}lo*r^hKnlqs�� e�okb.jsqdy{�ly~q.bdo�b.}�cie?�Au{osqdh�jsh)z|h¶t u{e��}lu~c.y{zUe�o�cie?r3eokb5bd}lr�osqR£l}3eUr�h)q.��}lo(¼ ÷ r ¢�v ¢£¥¤)¡ £�¤)¡¢ £

a�u©b.os�?}lglnlh�okb�y~zUrluÏ�� jky~cfh�r^h)qd��}loÅ� ÷Ì÷ Ãr�¢A�ÉÆxo%g�}lok±?hl�^u{e?b5jsh)glnAy{jsy~h)glokb5¦le?bdcfeh)qdnlosgw×�b.h?g�z�}A��bdosgljky{u{u{e?b:nlo�jkh)zUrAq.h)�3e1qs�va�u�z\�o�cfhKnlh%glh�osb8nlo�h?q.nlokg���r�h)q.��}lo¡1� B ¼ ¬ � ¬R� � � ë�@�ëIr ¡1�}� £Õ �)£���£¥Ãr&£4 

ê3ë ê��©ë~ö°ë ²`h)bÉz\�o�cfhKnlh)bpnlo*h)qdnlosg´£���nlo*h)qdnlosg<¡�q.osbdr^h?glnlosg<e|u~h)bÈcie1�lu{okq.h)b¢@ q @ q¼ � £�x ¼ �

¢@ q @ q£ex �q@[ � �q@[ �ïZ£

Page 80: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

jkh)g#¡§@ q tУ�x ¼ � v}Ãr&£)�:²`h|��}lo*n3e�u{}A��e?qpe�u{h?bpr3e?q.okb]okglj�e�·.e?nlh)b¢@ q @ q¼ � £�x ¼ �£ex �q@[ � �q@[ �ê3ë ê��©ë~ü°ë ºKy~¼ A r ¢�bdy{z|rlu{okzUokg�c.o�gAh�¦3e?jko�Ä e?u~cfeUz�}Au~cfy~rlu{y~j�e?qpr�h)qÇ�osuÏ�xaObmcfh�glhjkh)glbdc.y~c.}A�)o*r�h)qÉb��� z|y{b.z|h�}lgle|�)q.e?g�±)okg�cfe¥·.eA��r�osq.h�bdy©e?nlosz��e?be� A ��rȼ��Bosg�c.h)gljsokbØ A rp|~t�� � o㯠B ¼���z�l � o�¯ B ¼��LØ,��vZrÈ|~tL� � � � z�l � � � vÐz

nlo�zUhKnlh<��}lo¶Ø A jsh)y~gljsy~nlo�jkh)gÊosusØ � nlo�uwe�b.y{�?}ly{okg�c.o�yªcfosq.e?jsy��h)g°�#� okÄÅokjkcfh?b�nlosug��}lz|osqdh�nlo*h)r�osqfe1jsy{h?glosbpcfhKnlh�ÄÅ}lgljky{h)gle�jsh)z|h�b.y`b.o*cf}Z±Zy~osq.e�}Ag3e|o�cie?rle�z|osgAh)bs�ºZy`okg�oku`rlq.h)�Au{oszUe�e?g�cfokq.y~h)qpb.o*y{z|r�h)gloV¼ � rc@ q �`£òx»¼ � r ¢A�3oku°cie?�lu~osqdh�osb¢ £ ££ ¢£°)¡ £°)¡ê3ë ê��©ë¤�©ë »Ge1qdcfy~osglnAh|nAosu`cie?�Au{osqdh

¢@ q @ q¼ � oa¼ q ¼ � ¼ q¼ � ¼ q ¢¦ ¼ � ¦ ¼ q ¦ ¼ ÷u{e?b]jkh)glnly~jsy~h)glosb]nlo�h?q.nlokg>£�r3e?q.eUokuÂrlqdy{z|osq5z\�o�cfhKnlhU�Çu{e?b]nAo�h)qdnlosgÊ£%�#¡|r3e?qfeoku`b.os�?}lglnlh|b.o*cfq.e?nl}ljkosgÇosgÇuwe?bpokjs}3e?jky{h)gAosb¼ � oa¼ q r�£{z ¦ ¼ � o�¦ ¼ q o�¦ ¼ ÷ r £4z ¡HtL@ q ¦ ¼ q oÈt�¼ � oa¼ q v ¦ ¼ ÷ v�r £4 �5g3eUnlo%js}Z��e?b]b.h)u~}ljsy~h)glosb5osbM@ q r�£)� ¼ � rݼ q r�£°)¡K� ¦ ¼ � r ¦ ¼ ÷ r�£°)¡K� ¦ ¼ q r�¢A�Ȳ©h��}lo*jsh?q.q.okb.r�h)glnlo�e?u°cfe?�lu{okq.h

¢ £ ££ £�°)¡ £°?¡£�°)¡ £°?¡ ¢£�°)¡ ¢ £¥¤)¡ï)¡

Page 81: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ê3ë ê��©ëÍ�°ë ¬�h)glbdy{n8�okq.osbdo�jkh)z|h|zÊ�okc.hZnAhUnlo%e�±1e?gljko�oku`nlo�a�}lu~osqp��jkh)zUh|z\�okcfhKnlhr3e1qfe#jsh?g�c.q.h)u{e?q�okuposq.qdh)q�osu�nloÇaO}Au{osq�z|hKnly~Á3jse?nlhl�³a�uÈj�e1z��ly{h�nAo�r3e?b.h�±?osglnlql�en3e1nlh�jsh)z|h|e?g�cfosb5r�h)qe¯Hmr ¢*m ñ4¯�� ¢ m ¢A£°*ú)�»Ge1qdcfy~osglnAhUnloV�I�Âr ¢A�l*�sr&£)� ¤l{�Dr £?�lb.o*cfy~osglo� � r ¢ m £{z l � r&£ m £4z ¤l � r�£ m £)£�¢�¡s j j Y� ú ¡ ¢ m ¢A£�¢)¡7ze¯ m r ¢ m ¢4î{î4ñò j j 

¬�h)z|h|osuBosq.qdh)q5o�µZjsoknlo�¢*m ¢A£)��¦3e��Ç�K}Ao�nlokb.j�e1qdcie1q�osbmcfh)b]j`�e?u~js}lu~h)bÉ��q.osr�okc.y{qdu{h)bÉjsh?g¯Hmw�:ºKoxb.y~�)}lo�yªcfokqfe?glnAh�t jse?z��ly{e?glnlh�osuPrle?b.h�jse?n3e�±?osÃ�v:¦3e?bdcfe���}loxosu^osqdq.h)q8o�µZjsokn3eoku°cfh)u~osqfe1nlh� � r ¢ m ¢4î4×4ñò j T Nl � r £ m ¢4î4î4ñò j j  ¤l � r £ m ¢{ñ)Õ4ñò�����2� ú ¡ ¢ m ¢)¢4î)¢·¯ m r ¢ m ¢4î4î4ñò j T � q r ¢ m £ï4ï{îò j T Nl q r £ m £�ñ?�)�� j j  ¤l � r £ m ¡1¢4×?�������2� ú ¡ ¢ m ¢)¢4ñ)¢·¯ m r ¢ m ¢4î?�)�� j T � ÷ r ¢ m ¡?Õ�¡{×ò j T Nl ÷ r £ m ×A£�×)¢ò j j  ¤l ÷ r £ m ×)¡{×�¡s�����2� ú ¡ ¢ m ¢A£�¢�¡0¯ m r ¢ m ¢�ï4àZ£� j T Æxokb.j�e1qdcie1glnlh�u{e\�}luªcfy{zUe�y~c.osqfe1jsy��h?g|�Uq.okrly~c.y��osgAnlh)uwe�jkh)g¶¯Hmr ¢*m΢4ï4àZ£� j j :b.oxh?�Acfy~osglo� ÷ r ¢ m ¡4à{×)¢ò j T Nl ÷ r £ m ×)¢)¢)¢ò j j  ¤l ÷ r £ m ×?¢4îA£������2� ú ¡ ¢ m ¢)¢4î)¢·¯ m r ¢ m ¢�ï4à)¡s j T � " r ¢ m ×�¡{î4×ò j T Nl " r £ m ��¡)¡)¡s j j  ¤l " r £ m �4×A£às�����2� ú ¡ ¢ m ¢)¢4ñ�¡0¯ m r ¢ m ¢�ï?¢�¡s j T � � r ¢ m ×4ñ4î)Õò j T Nl � r £ m à4à{×�ïs j j  ¤l � r £ m à1Õ�¡{ñò�����2� ú ¡ ¢ m ¢)¢4ñA£²©e�j�e?g�c.y{n3e?n�nlo*h)r�osq.e?jsy~h)glokb5okbÉzUokglh)qposgÇosbmcfo%j�e?bdhl�

ê3ë ê��©ëÍ�°ë »Bh)qp}lg�rlqdh)�lu~oszUe�e?g�cfokq.y{h?qs�Aoku°z\�okcfhKnlh'«m�)qfe?gAnlos¯¶tÅosuPnAo�js}3e1c.q.h�o�cieM�r3e1bÚvUcfy~osglo�h?q.nlokg �l�ÙáÈe?bmcie\r^h)qUcie?g�cfhʱ?osq���}lo'osu�z\�okcfhKnlh�«dr�os��}lo� glh)¯Êcfy~osgloh)qdnlosg�¡Z��u{h%js}3e1u�bdo�qdosnl}ljkoxe%uwe?bOb.y~zUrAu{osbOjkh)zUrAq.h)�3e1jsy{h?glosb «í¼ ¬ r ¡�«í¼ ¬ @ ¬ r £)��]nlosz��e?bÉglh�cfy~osglo�h)qdnlosgd×�r^h)qd��}lo(× « ¼ ¬ @ q¬ Ãr £)�ê3ë ê��©ë � ë ²©e?b8jsh)gAnly{jkh)glosb�nloxh)qdnlosg�£���¡�e?rAu{y{jse?n3e?b8e�e?z���h)b:z\�o�cfhKnlh)b8y{z|rlu{y �jse?g ¼ � oa¼ q r £{z ¡*¼ q r £4z ¦ ¼ � o�¦ ¼ q o�¦ ¼ ÷ r £{z ¡R¦ ¼ q o�¦ ¼ ÷ r £4 

»Bh)q�cie1g�c.h�¼ � rÙ¼ q r £°?¡Z� ¦ ¼ ÷ rÞ£/x+¡R¦ ¼ q �C¦ ¼ � ré¦ ¼ q ��ºZyGe�osbmcie?b�okjs}3e?jky{h)gAosb�b.o�u~osbe� g3e1nlopuwe�jsh?glnly{jky��h)g�nlo5h)qdnlosg?×%nle?n3e*r^h)q�×*« ¦ ¼ ¬ @Ðq¬ r&£)��b.oÉcfy~osgloe× ¦ ¼ q o ÷" ¦ ¼ ÷ r�£É�nlo]e?��}`�� ¦ ¼ � r ¦ ¼ q r�£°1ÕA� ¦ ¼ ÷ r ��°1ÕA�v²©e�h1cfqfe�jkh)glnly~jsy��h?gUnlo5h)qdnlosg¥×A�KÕ « ¦ ¼ ¬ � ¬o� @ � r£)�©y~zUr�h)glo�Õ|¦ ¼ ÷ � qÌq @ q r×£)�Bu{h���}lo|u{u{o�±1e�e?u��}lgly{jkh�cie?�lu~osqdh\t }lb.e?glnlh�uwe�jsh)gAnly{jky��h)gnlo*bd}lz�e�r�h)qÈÁ3u{e?bÚv

ï{×

Page 82: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

¢ £ ££°)¡ £°1� £�°1�£°)¡ £�°)¡ ¢£°?Õ £�°?Õ ��°?ÕÌÎÍ ê3ëYê��©ëÍ °ë tÏÓxz|y~cfy~nlh�vÑ�

9�Ü :=< â¥>)@sàÅB é�ä äGáDC6Eö°ë ê�ë ê3ë ²`h)b�e1}Acfh�±1e?u{h?q.osb�nlo�uwe�zUe1c.q.y{Ã�b.h)g « � r;x%£�� « q r;x3×A�Åá�}lbdj�e?glnAhbdh)u{}ljky{h)gAosb�gAh�cfq.yª±Kywe?u~osb5nlo�t O x « ���Hv \ò1��r \¢�b.o�bdy{�)}lo��K}Ao \ò � r;tУ4zjx%£v ­ � \ò q rtY¡7zjx%£v ­ ÄÅh)q.zUe?g�}lgle|�3e1b.o*nlo%e?}Ac.h¥±?osj�cfh)qdosbs�8a�b]nAosjsy~qO r ì x3à x5�¡ £?ð ríì £ ¡x%£ x%£�ð ì x�£ ¢¢ x3×�ð ì £ ¡x�£ x%£�ð � � rc´Y¨g´0� �  

a�u`z\�okcfhKnlh�nlo%a�}lu~osqÉjsh)gÛ¯wr&£%okbl � � � r¹l � o O l � rÙt��VoP¯ O v�l � r�´?t��3o�¨âvo´ � � l � z

��}lo*y~c.osq.e?nlh�y{z|rlu{y~j�el � rc´?t��±o�¨âvÌ�,´�� � l�tY¢�v�r�´ ì ¢ ¢¢ tyxx¡4v � ð ´�� � l�tY¢�vР

ºZy[´ � � l�tY¢4v�osbÉ}lg�±)osj�cfh)q5nlo*jsh?q.nlokg3e?n3e?b « �,\'okg�c.h)gljkosbl � r�´kì ¢t�x�¡4v � \üð z

��u{e+�}lgly{jse�ÄÅh)q.zUe�nlo*��}lo%b.o*js}lz|rlu{e�u~y{z»l � r ¢�osbÉ��}lo-\dr ¢Z����nlokz+�e?b´0� � l�tY¢4v~ríì « ¢Hð � l�tY¢4vNr « ´kì £¢*ð � lut ¢�v~r « \ò �  a�gÇosb.o%j�e1b.h·l � okb5y~n8�osg�c.y{j�e1zUokg�c.o�g�}lu{h�r3e?q.e0¢\À £)�

ï1�

Page 83: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ö°ë ê�ë~ö°ë ºZo�e \ò�okuAe?}Zcfh�±)okjkcfh?q�nloÈ}lg�e?}Zcfh�±1e?u{h)q « ��bdo�eròZ�lb.}�jkhZh?q.nlokg3e?n3exzUe��)h)qokgDZ1e?u~h)qpe?�lbdh)u{}Zcfhl�O²©e_D¡x��osbdy{zUe�jkhZh?q.nlokg3e?n3e�nlo*uwe�okjs}3e?jky��h)g)t O x « �7v \ò�r \¢�osb�C� � ò � o¹�����oa�C��� � � òZ� � � o¿t��C���Ix « voòZ�7oP�C���Þ� � ò1��� � o¹�����joP�C� � ò � r ¢Hz��}lo%e?rlu~y{jse?glnlh�u{e�nAosb.y~�)}3e?u~n3e?n�c.q.ywe1gl�)}lu{e?qÈu{u~ok±1e�e� « x��C������� ò1����ß�� �C� � ò � o������jo �C��� � � òZ� � � o»�C����� � òZ��� � o������To»�C� � ò � ��ß�� òZ�¡� B ¬�¬2 � � �C� ¬ �  ºZy~zUrAu{y~Álj�e?glnAh�ò1�Ï�3b.o�cfy~osglo*��}lo « ¦¥¨��Ò�

ö°ë ê�ë~ü°ë ºZos���}lg�osuÉcfokh)q.okz�e'nloÇu{h)b|j?�� q.jk}lu{h)b�nlo<¾�osq.bd¦l�)h)qdy{g°�8u{h)b|e?}Zcfh�±1e?u{h)qdosb« � z « q js}AzUrlu~osg�� « �ux������üßØ£|r3e?q.eÇjky{okqdcfh?bY� � z�� q ¦Ýtyx�£{z�£v��©r�h)q�cie?g�c.h»� « ��� æ¡Z�زBe\b.h?u{}ljky��h)g o�µAe?j�cieË�Ôu{ea¢1x��okb.y{zUe\y~cfokqfe?jky��h)g nloku%zÊ�okc.hZnAhËnlo³a�}lu{okq�bdh)g°�qdosb.r�osj�cfyª±?e1zUokg�c.o?�l�tL�]vNrc´ ì ú�] � � ¢¢ ú ] � � ð \�hz l � r�´ ì tУÂo « � ¯ v � ¢¢ tm£Do « q ¯Iv � ð \�

jkh)g \��r ´ � �Ìl�tY¢�vÑ��ºZyÂu{y~z ��­ � 0 l�tL�]vòr ¢U�<u{eJD�x��okb.y{zUe�jshKh)qdnlosg3e1n3e�t}DDrÿ£4zÑ¡4vokb�glh#g�}lu{eA��glosjkosb.e?q.y{e?zUokg�cfo « � æ ¢A�G�³jsh)z|hã� « �¡� æ ¡Z�òtm£/o « �L¯Iv � ¾ ¢�r3e?qfejk}3e?u{��}ly~osq±¯ æ £?�*Óx��±Ky{e?zUokg�cfo?�^b.yÂuweJD�x��okb.y~z�e�jkhZh?q.nlokg3e?n3e�okbxg�}luweZ�Ntm£so « ��¯Iv �e?rle?q.okjso�z�}lu~c.y{rlu~y{j�e1nlh�r^h?q5jkosqdhl��a�g�js}3e?u~��}ly{okq]jse?b.h�u~y{z ��­ � 0 l�tL�]vÂr&¢Uy~zUrAu{y{jseu~y{z»l � r ¢A�ö°ë ê�ë¤�©ë ²`h)b*e1}Acfh�±1e?u{h?q.osb�b.h)g»x%£��Ax�¡�jkh)g'u{h�jk}3e?u�e1uve?rlu~y{jse?q�okuvz\�o�cfhKnlh�nloa�}lu~osq l � � � r�t��VoP¯ O v�l � rc´ ì �VoP¯ ì x�¡ ¢¢ x�£ ð3ð ´ � � l �  ��jkh)zUh|e?g�c.osbs� l � rc´�ì tУex�¡{¯ v � ¢¢ tm£�x»¯Iv � ð ´�� � l{�

��}lo�c.y{osgAnlo�e�jsokq.h�r3e?q.e�cfhKnlh�¢ æ ¯ æ £)��²©e�qfe?ð�h)g'osb���}lo�u~h)b�e?}Ac.h�±?e1u{h)qdosbxnlo}lgle�zUe1c.q.y{Ã�jsh)gÇosu~osz|osg�cfh)bÉ�)q.e?glnlokbÉrl}losnAosg<bdosqÉr�os��}lo� glh?bs�ÌÎÍ ö°ëYê3ëÍ�°ë tÏÓxz|y~c.y{nlh�vÑ�

ï4à

Page 84: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ö°ë~ö`ë ê3ë �]u©e?rlu{y~j�e?q8osu`z\�okc.hZnlh|e0l m r « l��l � � � r¹l � o « ¯ l � oal � � �¡ � l � � � r ¡�o㯠«¡3xa¯ « l �  

»Bh)qÉjsh)glbdy{�)}Ay{osg�c.o�osu`nlh)z|y{gAy{h�nlo*okbdcie1�ly{u~y{n3e?n�u~y{glose?uPokb²�r_^¢%·¦a` t ùù ¡�o�%¡±xv% ùù æ £cb0r -#®5oH% æ ¢ /� 

²©eË�}luªcfy{zUe*y{�)}3e1u{n3e?n�b.o�rl}loknlo�nloknl}ljsy~qÉe?u{�?os�lq.e?y{jse?zUokg�cfo�okb.jkq.y{�Ay{osgAnlh�%År��.o�DÇlh*nlopzUe?glokqfe��)osh?z\�o�cfq.y~j�e�qdosrlqdosbdosg�cie?gAnlh�u~h)b�gx�}lz|osq.h?bvjsh)z|rlu~oзdh)bvjkh)z|h*±?osj�cfh)qdosbst%*osbmc��e*osg|osu3b.okzUy~rluwe1glh�y{Ãk�K}Ay{osqdnlh*b.yl��bl�h)u{h*bdy�%*�|¡�ÄÅh)qdz�e1g|}Ag��e1gl�)}lu~h%h?�Acf}lbdhl��u{h��}lo�ok�K}Ay~±1e?u{o�t qdosjs}8�osq.nAosb.o*u{e�q.ok�)uwe�nlosu^r3e?qfe1u{osu~h)�)q.e?zUh�vve��K}Ao%¡Do�%�z|y{n3e%zUokglh)b��}lo�¡±xv%A�ö°ë~ö`ë~ö°ë a�u`nlh)z|y{gAy{h�nlo*okbdcie1�ly{u~y{n3e?n�u~y{glose?uPnAosu`z\�okcfhKnlh�nlo%a�}lu{okqpzUoE·dh)qfe1nlh�osb²�rå-1%·¦d` t��ª¯·t}%�v� æ £§/ jsh)g�¯·tL%4vZr�£Âo°%3o %{q

¡  �5g>�)y{qdh�nAo<£�î)¢ � e?u~q.osnAosnlh)q%nlol%�r x�£�±Ky~osgloUn3e?nlh�r^h)q�%aG ¾ x�¡�x�%A�<¬�h)zUh¯·tyxx¡?x�%�v�r ¯·tL%4vÛt u~h³jk}3e?u5b.o�q.osnA}ljso<e³}lg+bdy{z|rlu{o�j°�e?u{jk}lu{h�v�oku5nAh)zUy~gly{h'nlookbdcie1�ly{u~y{n3e?n�u{y{gAo�e?u°okbÉy{g�±1e?q.y{e?g�cfo�r�h)qposbmcfo�cfy~r^h�nlo*�)y~q.h)bk�ÆxoÇuwe'zUy~b.zUe'ÄÅh)qdz�eZ�(� ¯·tL%�v��sr �ª¯·t %4v�Ge?b��� ��}lo�cfe?z��ly��osg�osb�bdy{z\�okc.q.y{jkh³r�h)q®Ez®%.r ¢A�O§Ây{g3e?u~zUokg�cfo?�Kcfq.e?bÉ}lglh)bÉj`�e1u{js}Au{h)b¯·t�x%£Do°��ovDÇlHvNr �#q�oÔ£�x l7q

¡ ovDi�#l] ¬�}A�?h�z+�h?nl}lu{h%osb�y{g�±1e?q.y{e?g�cfo]e?u^jse?z��ly{e?q���r�h)qexM�K�OÆxo�z|hKnlh���}lo�osuPnAh)zUy~gly{h*nlookbdcie1�ly{u~y{n3e?n|u{y~glo�e1u�cfe?z��ly��osgUosbÈy~g�±1e?qdywe?g�c.o]r�h)q�u{e%c.qfe?glbmÄÅh)q.zUe?jky��h)g¶x�£�oÝ�NoÝDÇl8G ¾x%£�xd��o°D�l���}lo*jsh)qdq.osbdr^h?glnlo�e�}Ag3e|bdy{z|okc.q��� e�r^h)qpu{e�q.osj�cieh®5oK%.r�x%£)�

ö°ë~ö`ë~ü°ë e�vx²©e�q.ok�)uwe�nlokuvcfq.e?r^okjsy~h��#osu�z\�okcfhKnlh�y~zUrluÏ�� jky~cfhUnlosu�okg�}lgljsy{e?nlhÇy{z��rlu~y{jse?g°�le1u`b.osq5e?rAu{y{jse?nlh)bÈe·l�m7r « l^�Auwe?bÈÄ1�h)qdz�}lu{e?bÈnlo*q.okjs}lqdq.okgljsy{el � � � r ¡eoP¯ «¡Vx ¯ « l � z l � � � r £

¡±xa¯ « l �  av±Ky{nlokg�cfosz|osg�c.owtY¡eo°%�v¡°HtÏ¡±xv%�v�¾ x%£*��£°tУex�%�vD¾ ¢A�

ï?Õ

Page 85: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�Ivp²©e�±)osqdn3e?nlokqfe|b.h)u~}ljsy��h)g�nlo}l m r « l�jk}lz|rlu{ol�tL� � � � vl�tL� � v r ú�]?ß � � � > � lut ¢�vú ] � � lut ¢�v r¿ú ]�>  ºZy�x/®5o « osb��)qfe?gAnloUokg>jsh?zUr3e1qfe?jky��h)g'jsh?g»¯ � �Ñ�~ú�]�>�okb�z�}A�'r�os��}lo� glhl�Gjkh)g"}Agnlokj�e?y~zUy~osg�cfh�q3�e?rAy{nlh�b.os���}Ag»®5o « ¯a¾ xG �'²`h)b�zÊ�okc.hZnAh)b�ªòx5osbdcfe?�lu~osb�y{z|y~cfe?gokbdcfo*nlokj�e?y~zUy~osg�cfh��)e|��}lol � � �l � r�¯·t « ¯IvN¾ ¢ js}3e?gAnlh¥®Éo « ¯w¾ xG¿ 

ö°ë~ö`ë¤�©ë ²`h)bxe?}Acfh�±1e?u~h)q.okb�nlo�u{e�zUe1cfqdy{Ã%nlosuÂosg�}lgljkywe?nlh�bdh)g x�¡?¢��)x%£)�%a�g�uwe�3e1b.o�nlo�u~h)b�e1}Acfh�±)okjkc.h)q.okb|okbdc.o�rlq.h)�Au{oszUe�±?osjkc.h)q.y{e?u�bdo�«dnlokbfe?jkh)rluwe1¯#osg\u{h?b�nlh)brlqdh)�lu~oszUe?bÈosbdj�e?u{e?q.okb/l�m7r�x�¡?¢{l��l�m7r�xel^�O»Bh)qpcie?g�cfh�oku`b.}lrlqdosz|hUr�osnAy{nlh�osbôêr bd}lr -*¯åt��ª¯·tyxx¡1¢�¯Iv� æ £4zV� ¯·t�x3¯ v�� æ £,/� ²©epÄÅ}lgljsy��h)g%nlo:e?zUrAu{y~Álj�e?jky��h)gx±Ky{okgloOn3e?n3e5r^h?q�¯·t��]v�r�£{o(��o(� q °)¡j{èo(� ÷ °{×!{èo}� " °1�#{��}lo´osb�}lg r�h)u{y~glh)z|y{h³�K}Ao³cfy~osglnAo"ePo³ js}le?glnlha�ä¾ xr ��c.y{okglnlo´e £ �jk}3e?glnlh��é¾ ¢ � ¸�e1b��� ��}lo�oѵAy~bdc.y{q3�e�}lg>±1e?u{h)q�z��� gly{z|h��I� æ ¢#jsh)g°¯·tL�I�Úvhr £)�cfe?uO�K}Ao]¯·tL�]v æ £Uosg�tyxr¿z��I�Äv��³¢ æ ¯·t��]v æ £�okg¹tL�I�jz¡�I�Âofe�ÞÏ�<ºZy8e?nlosz��e?b� ¯·tL�I�а)¡1¢�v� æ £)�Zbdo]c.y{osgAo]glokjsokbfe?qdywe?z|osg�cfoMôêr�x��I�Ä°)¡?¢A��a�gUnlokÁ3gAy~cfyª±1eA��¦3e��U��}lo�l}Ab.j�e1q5u{e�zUokglh)qpqfeA�� Ãxglok��e1c.y~±1eA�H�I���lnAo�u{e�osjs}le?jsy��h)g

£Zo»�0o �Iq¡j{ o � ÷× { o � "�!{ r £4 ²`h���}lo�ok��}ly~±1e?u~o?�loku{y{z|y{gle?glnlh�uwe�qfeA�� Ã�cfqdy~±Kywe1u]��r ¢A�3e�¦3e?u{u{e?q�u{e�zUokglh)qpq.el�� Ã�nlo�I÷�o��{� q o £�¡#�0oË¡1�År ¢H a�uOrlq.y~zUokq�zUy~osz��Aq.h�osb�}lg3eÇÄÅ}Agljsy��h)g³jkq.okjsy{okg�cfoâ|B�Ge?bs�� �K}Aoâ|~t��]v(r ¢Çcfy~osglo�}lglebdh)uwe�q.el�� Ã1�:¬�h)g��Ay{b.okjsjky{h)glokbÉb.}ljkosb.yª±1e?b|~t�x/×�v æ ¢ æ |�t�x�¡4vÄz |~tyxx¡ m î�v æ ¢ æ |~tyxx¡ m à4vÐz |�t�x�¡ m ï{ñ4v æ ¢ æ |~t�x�¡ m ï{î�vÄ »Bh)qUcfe?g�cfh��I��r x�¡#m¤ï{ñ�o�g'jsh?g�¢ æ g æ ¢*m ¢A£ tÅ}lg+j`�e1u{js}Au{h´jsh)z|rlq.}Aos�3e"��}lo� ¯·tL�I�а)¡1¢�v� æ £v��:Æxo�z|hZnlh���}loôêr ¡#m¤ï*ñ

¡?¢ o ¤ g}r ¢ m £�×4ñ�àòo ¤ g jkh)g»� ¤ g� æ ¢ m ¢)¢)¢�à7 ï4ï

Page 86: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

a�bdc.h�e1rlq.h�µZy{zUe_ô jsh)gÇ}lgÇosq.qdh)qpq.okuwe1c.y~±?h|z|osgAh)qp��}lo*osu�£¥Ö��ÌÎÍ ö°ë{ö°ëÍ�°ë tÏÓxz|y~c.y{nlh�vÑ�ö°ë~ü`ë ê3ë áÈe?bdcfe�osz|rlu{ose?q�u{e�Ä1�h)qdz�}luwe%��}lo�nlokÁlglo�osu^z\�o�cfhKnlh�nlo*a�}lu~osqÈz|oзdh)q.e?nlhh�}Zcfy{u~y{Ãse?qÉ�K}Ao�osbx}Ag�z\�o�cfhKnlh�oѵArAuÒ�� jky~c.h�nlo�nAh)b�o�cie?r3e1b��<h?q.nlokg´¡Ur3e?q.e�jsh)gAjsu{}Ay{q��}lo ¯·t}%�vDr&£Do�%/o %{q

¡  ö°ë~ü`ë~ö°ë ºZy`}Ag�z\�okc.hZnlh�okb]jkh)glbdy{bdc.osg�cfo_\¼ ­ \£/r £)�A��r�h)qÈcfe?g�cfh¯·t}%�v�r £Do�% \¼ ­ t��.x O %�v � � \£±r&£Do�% \¼ ­ \£DoPÆwt}% q v�r�£Do°%3oaÆwtL% q vÄz

jkh)zUh�eMÁ3q.zUe�uwe�y{gAnly{jkywe?jky��h)g°�ºZok�È�}lg�osbdcfe�Ä1�h?q.z�}lu{eA�Arle?qfe=e�À�¢�b.}AÁ3jky{okg�c.osz|osg�cfo�r^ok��}lo� glhl�3bdo�cfy{okglo¯·t�xheÚvDr&£�xie1oaÆwtKe q v æ £ æ £Do�e1oPÆ¥t�e q vNr�¯·t�eÚvР»Bh)q]cfe?g�cfh�xhe(¦Ý²×�jehæü²ånlh?glnlo<²åokbxosuÂnlh)z|y{gly~h|nAo�osbmcie?�ly~u{y~n3e?n<u~y{glose?uÏ�5ÆxozUe?glokqfeU��}lo�¢�¦ ²×�<¢â¦Ê§3qTt�²?vÑ����nAosz��e?bxjsh?glb.y~nlosq.e?glnlh�}Ag�r^ok�K}AoK glh�okg�c.h)q.gAhe?�Ay{osqmcfh�nloJeÉnly{b ·d}lg�cfh|jsh)ga²��lbdo*c.y{okglo%¢·¦ ²%k tK`ãx ²?vNr §3qTt ²?vÑ�

ö°ë~ü`ë~ü°ë ºZy`}Ag�z\�okc.hZnlh�okb]nAo%h?q.nlokg Ê osg�c.h)gljsokb¯·tL%4vZr�£Âo°%3o % q¡j{ o¹������o % ÉÊ { oaÆwt}% É � � vÄ 

»Bh)qGh?c.qfe5r3e?qdc.o?�)u{eÉÄÅ}Agljsy��h)g�nlo�e?zUrAu{y~Álj�e?jky��h)g*nlo8}lg�z\�okcfhKnlh]o�µZrluÏ�� jsyªcfh5nlosEÈokcfe?r3e?bokb�}lg³r^h)u~y{glh?zUy~h�nlo��?qfe?nlhÇz|osglh)q%h<y~�)}3e?u���}logE)��aObmcie?b�nlh)b�rlq.h)rAy{osnle?nlosb%b.h?gjkh)zUrle1cfy~�lu{okbÈb3�h)u~h�b.y Ê ß�E)�Á ö°ë~ü`ë¤� ºKo*c.y{okglo*uwe�y{nAosg�cfy~n3e?ntL�Åxv% O vTt��±o�% O o°% q O q o¹�����o°% � O � v�r¹�.xv% � � � O � � �  

®Eg�±Ky{qmcfy{okglnlh���nlokb.r�oз.e?gAnlh�tL�Åxd% O v � �tL�Åxv% O v � � r0tL�Vo°% O o�% q O q o������o�% � O � vTt��.xd% � � � O � � � v � �r0tL�Vo°% O o�% q O q o������o�% � O � vTt��±oPÆ¥tL% � � � v¡vr3�±o�% O o°% q O q o¹�����o°% � O � oPÆ¥tL% � � � vÄ ï{î

Page 87: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

Æxh)gAnlo�uweÇy{�)}le?u{n3e1nét��¥x5% � � � O � � � v � � r �·oÈÆ¥tL% � � � v�b.o�rl}Aosnlo�nloknl}ljky{qs��r�h)qoE·dosz|rlu{hl�Znlo*uwe�Ä1�h)qdz�}luwe�¦3e?�lyªcf}3e?uPr3e?qfe�oku`j`�e?u~js}lu~h|nAo%u{e�y{g�±)okq.b.eA�ö°ë~ü`ëÍ�°ë ºZok�È�}lg�osu`rlqdh)�lu~oszUe�e?g�cfosqdy{h)qpjkh)gÛØ?r&£)�

£Do�% \¼ ­ t��(xv% O vÚ� � \£3r�£Do�%/o %{q¡ oPÆ¥tL%{÷Äv

ok�K}Ay~±1e?u{o*e o³%j\¼ ­ tL�Vo�% O v \£3r�£Do°%3o % q¡  ®E�)}le?uwe?gAnlhUjkhZo�Á3jsy~osg�cfokbs�°okbdc.h�osb�u~h�z|y{bdzUh���}lo�u{e?b]jkh)glnly~jsy~h)glosb]nlo�h?q.nlokg>£��<¡Zt\¼ ­ \£/r £)��¡ \¼ ­LO \£±r&£)�

ö°ë~ü`ëÍ�°ë a�u`z\�okcfhKnlh�glh�osbÉnlo*h)qdnlosgd×�r^h)qd��}lo*glh�b.o%js}lz|rlu{o}×*«X¼ ¬ @Ðq¬ r�£)�»Ge1qfe�j�e?u~js}lu{e?qÈuwe�ÄÅ}Agljsy��h)g�nlo%e?zUrAu{y~Álj�e?jky��h)g°�Kb.o%jsh?glb.y~nlosq.etL�Åxv% O vÚ� � \£3r ÊÌ £ ¢ ¢%�°)¡ £ ¢%{qÄ°?Õ %�°{× £

ÍÏ \£/r ÊÌ ££Zo�%�°?¡£Âo°%�°{×eo�%*qT°1Õ ÍÏ  »Bh)qpcie?g�cfh¯·tL%4vDr&£Âo°%��1x £× o £× tm£Do %

¡ vüo¿tm£Do %× o %{qÕ v � r £Do�%/o %{q

¡ o % ÷Õ  � ö°ë~ü°ë � ºZy{okzUrAq.o���}lo�}Ag�z\�o�cfhKnlh�b.ose�nlo�h)q.nAosg Ê r3e?q.e�osuÂrlq.h)�Au{oszUe�okb.j�e1uwe?ql�mer « l���b.oÇcfokglnlq3�eü�t}%�vâr £}o %0o������7o %TÉ*° Ê {7oÝÆwt}%TÉ � ��v��Ô»Bh)qUoku{u~h´�le?bdcfenlokzUh?bdcfq.e?q:�K}Aox¦3e��|z\�o�cfhKnlh)b:�K}Ao�cfy~osglokg�h)q.nAosg Ê rle?qfe%nly{ji¦lh�rlq.h)�Au{oszUe*r^okq.h�glhokg��)okglosq.e?uÏ�ºZose³osuÉz\�okc.hZnlh´o�µZrluÏ�� jky~cfh'jkh)g Ê okcfe?r3e?bU�K}AoÇc.y{osgAoÛ�C� ¬ r £Çb.yKD æ N3�+²`h)bnlyªÄÅosqdosgljkywe?u~osbxoku{osz|osg�cfe?u{okb�r3e?qfe�okuvrlq.h?�lu{okz�ewl m r « l<b.h?g´c.hZnlh?b�gK}Au{h)b�oѵAjkosrAc.hu~h)bp��}lo*jsh)qdq.osbdr^h?glnlosg<e�u{h)bÇ�e?qd�^h?u{osbpu~y{glose?u{okbs�OºKyu�ÈosbÉoku%�e?q.��h)u°u~y{glose?uPnlo*h)qdnlosg��$ ¬ tL��vNr B¬ ��l ?/?/? l ¬ ; � ¬Ç¬ � � ¬ � ¬)(  j j ¡� ¬ ; � � ¬ ;ÂrXì N.x+£�±x�£ ð z

okg�c.osglnAy{osgAnlh�okbdcfo]gx�}lz|osq.h*jkh)z��ly~g3e1cfh?q.y{h�jsh)z|h�jkosqdh�b.y��0À�N3��»Âh)qOcie1g�c.h�oku{y~�)y{okgZ�nlh�u~h)b�¼ ¬ nlo*z�e?gAosqfe���}lo�j{ ÉB ¬ 2 � ¼ ¬ ì N(x+£�±x�£ ð r�£4z �}r £4zÑ¡nzj j j Äz Ê ¸ï{ñ

Page 88: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

okuKzÊ�okc.hZnAhÉc.osglnAq3�e]h?q.nlokg Ê rle?qfe�l m r « l��BaObmcfo8b.y{bmcfokz�epcfy~osglo:b.h)u~}ljsy��h)g?t bd}�zUe1cfqdy{Ãokb�cfqdywe?gl�?}luwe?qÉglh�b.y{gA�)}luwe1qÚv��5��nAosz��e?bxosuÂz\�o�cfhKnlh�h?�Acfokgly{nlh�glh�cfy~osglo�h)q.nAosg Ê okg�)okglosq.e?u`r�h)q.��}lo�Ä e?u~uwe?g�u{e?bpjsh?glnly{jky{h)gAosbpnlo%h)q.nAosg°�O»Bh)qÉoзdosz|rlu~h× ÉB ¬ 2 � ¼ ¬ @ q¬ r¹× ÉB ¬ 2 � ¼ ¬ t N(x�£v q r¿× ÉB ¬ 2 � ¼ ¬ ì ¡ ì N.x�£¡ ð o ì N.x+££ ð3ð z

��}lo*b.ok�È�}lgÇuwe�osu~osjkjsy��h?gÇnAo%u~h)b�¼ ¬ osb5ÕV��£°{×!{joP×V��£°)¡j{üÃr £)�ö°ë~ü`ëÍ °ë a�u°cie1�lu{okq.h�nlosu`zÊ�okc.hZnAh�b.osql�e|nAo%u{e�ÄÅh)q.zUe

£ £ ¢¸�oaº ¸ º£�x»¼ ¼ºZo�rA}losnlo%b.}Ar^h)gAosqe¼�Ãr ¢���¸wo»ºãÃr £)�A�)e|��}lo*osgÇh?c.q.h�j�e1b.h|glh�r^hKnlqs�� e�±)okq.yªÁ3j�e?qu{e�jsh)glnAy{jsy��h)g�nlo*h)q.nAosg<¡Z�²©e�ÄÅ}lgljsy��h)g�nlo�e?zUrAu{y~Álj�e?jky��h)gl¯·tL%�vÈosb

£Do�% \¼ ­ ì £�xd% ¢x/¸ % £�x ºÑ% ð � � \£3r�£Do % \¼ ­tm£òxv%4vTtm£exAºÑ%�v ì £ex ºÑ% ¢¸ % £�xv% ð \£r�£Do�% £Do¿t�¼#t�¸�x�£v�xAºDtУex»¼Äv�vR%tm£òxv%�v6tm£exAºÑ%�v  

ºZyVºgr ¢A��r�h)q�uwe1b�q.osnA}ljsjky{h)glokb<y~gly{jkywe?u~osbâ¼ Ãr ¢\�¹¸ Ãr £)�xnlo´zUe?glosq.e���}lou~y{z°¯·tL%�v�r� �:ºKyüº�Ãr ¢u{y~z�¯·t}%�vZr�£Do ¼#t�¸�x�£�v�x ºÂtУòx»¼Ävº r £�x»¼~oP¼#t�¸do»º1v1x�£º r x�£

¡*º Ãr ¢7znlh?glnlo*b.o*¦3e�}lbfe1nlhUu{e�jsh)gAnly{jky��h)g�nlo*h)qdnlosg<¡Z�°£�x»¼~oa¼#t�¸¶oaº1vNr�£�°)¡Z�

ö°ë~ü`ëÍ&°ë �Âq.e?b]e?u{�)}Aglh)bÉj`�e?u~js}lu~h)b5b.o%jsh)z|rlq.}Aos�3e|�K}Ao�osuBz\�okcfhKnlh|osb]nlo�h?q.nlokg�×A�¬�h)z|h�osbÉo�µZrluÏ�� jky~cfhA�Auwe�ÄÅ}Agljsy��h)g�nlo�e1zUrlu~y~Á3jse?jsy��h)g�okb¯·tL%4vZr�£Zo�%/o % q¡ o % ÷Õ  

Æxo�z|hZnAh��K}Ao ¯·t�D���v�r�£�x �yq¡ o°D��§�f£�x �yqÕM�  î)¢

Page 89: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�]b��� rl}lokbs��r�h)qpoзdokzUrlu~h��ª¯·t��³D ç ¡4v�*r ¡ ç ¡{°{× æ £)�A�N�|D ç ¡0¦�²��� ö°ë~ü°ëYê�+ ²©e�ÄÅ}lgljky��h)g�nlo%e?z|rlu~y~Á3jse?jsy��h)g�b.okq3�e�nlo*uwe�ÄÅh)qdz�e¯·t}%�v�r ´?tL%4v

£òx»� �Ì� %nlh?glnloY´�osbÉ}lgÇr�h)u{y~glh)z|y{h�qdo�e?uY�ºZy��)q�´ÙÀ £]osg�cfh?gljsokbÈu{y~z_± ­ 0 ¯·t}%�vDrc �|osu�nlh)z|y{gly~h*nlo]okbdcfe?�ly{u~y{n3e1nUu~y{glose?u² osb�e?jsh1cie?nlhA��ºKy��)q³´ r ¢�okg�cfh)gljkosbY²Úokb�oku�o�µKcfokq.y{h?q%nAoU}lgleÇjky{q.jk}lgAÄÅokq.osgAjsywe�¼£/x°%4� �Ì� �nr�j�cfo)�]»Âh?q�cie?g�c.h�uweÔ�}lgly{jseUr�h)b.y~�ly{u~y{n3e1nÇokb��)qK´Ùr £)�5��nAosz��e?b�jkh)zUh¯·t ¢�vNr £)�lnAos��o%bdosq ¯·tL%4vDr £DoaºÑ%

£ex»� �Ì� %  ºZym² r -#®Éo % æ ¢ /��:glosjkosbfe1q.ywe1zUokg�c.oa� ¯·t}D���v��r £Çr3e?q.e��¶¦ §��:jsh?gËu~h´jk}3e?uº�rm�(� �Ì� tÅr3e?qfe´osu~u{h´�3e?bdcfe³cfh?z�e?q0�â¾ év�� a�uÉj�e?bdhAºkr x/� �Ì� u{u~ok±1e³e´uwejkh)g�cfqfe1nly{jkjsy��h?ga²�rfnl�:»Bh)qpcie?g�cfh�u{e+�}Agly{jse�r�h)bdy{�ly~u{y{nle?n�okbeº�rÈ� �Ì� �¯·tL%�v�r £Doa� �Ì� %£òx»� �Ì� % r�x%£Âo ¡£�x»� �Ì� % r £Do�¡*� �Ì� %3oË¡{� q �Ì� % q oË¡{��÷ �Ì� %{÷�oPÆwt}%§"6vÄ 

ºZy�osu^z\�o�cfhKnlh�okbÈjsh?glb.y~bdcfokg�cfo?�#¯·tL%�vZr�£�oü%Do�Æ¥tL% q v/t r�h)q.��}loY\¼ ­ \£/r £vÑ�ZnAoxzUhKnlh��}lo(� �Ì� r&£°)¡�� ¯·t}%�v�r ¡�o�%¡3xv% r £Do�%/o %{q

¡ o % ÷� oPÆ¥tL% " vР»Bh)qO}lg�rlq.h)�Au{oszUe�e?g�cfokq.y~h)qs�¢¯·t}%�vDr&£]o�%�o�%{qÚ°)¡�odÆwt}% ÷ vGy~zUrlu~y{jse]��}lo5osu3z\�okcfhKnlhokbpnlo�h)q.nAosg�¡Z�O­]h�okbÉnlo�h)q.nAosg¶×�r^h?q.��}lo³¯·tL%4v}Ãr�£�o�%�od%{qÄ°)¡sod% ÷ °?ÕÂo ÆwtL% " v��

ö°ë~ü`ë ê�ê3ë ²©e�ÄÅ}lgljsy��h)g�nlo%e?z|rlu{yªÁ3j�e?jky��h)g�osb¯·tL%4vZr�£Zo�%�� ¢ £ � ì £�xd%�°?¡ xM%�°)¡%�°?¡ £òx»×C%�°?¡{ð � � ì ££Tð��}lo�nlokb.rl}8�osb5nlo�okÄÅokjkcf}le?qÉu{h)b8j`�e?u~js}lu~h)bÈu{u~ok±1e�e_¯·t}%�vDr&£°tУsx�%4v��:a�u°nlh)z|y{gly~h�nlookbdcie1�ly{u~y{n3e?n�u{y{gAo�e?u°okbÉuwe�q.ok�)y��h?gÇoѵKcfosqdy{h)qÉe�uwe�jky{qdjs}lgAÄÅokq.okgljsy{eJ� %}x�£7�*r�£

îA£

Page 90: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

»Bh)qpcie?g�cfh_²�o -#®5oK% æ ¢ /%��osu`zÊ�okc.hZnAh|okb O x5osbdcfe?�lu~o?�ö°ë~ü`ë êKö°ë �Bqfe?b*e1u{�)}lgAh)bxj`�e1u{js}Au{h)b]b.o�rlqd}los�3e���}lo�uwe|ÄÅ}lgljsy��h)g�nlo�e1zUrlu~y~Á3jse?jsy��h)gokb ¯·tL%4vZr�£Âo°%Y� �q �q � ì £ ¢xG%�°?¡ £òxv%�°)¡*ð � � ì ££�ð r ¡�o�%

¡±xv%  ºZok�È�}lg�bdo�±Ky{h�okg�}lg�rlq.h?�lu{okz�e�e?g�cfosqdy{h)q:uwe�q.os�?y��h)g\�¤tÏ¡�o�%4v¡°tY¡�x %�v�� æ £xjsh?y{gljky{nlooѵle1jkcie1zUokg�c.o"jkh)g oku%bdosz|y{rlu{e?glh\y{Ãk��}ly{okq.nlhl�]�Ôosg jkh)glb.okjs}lokgljsy{e�osu*z\�okc.hZnlh�osbO x]okbdcie1�lu{o1�

ö°ë~ü`ë êKü°ë ºZy~�)}ly{okglnlh�u{e�y~glnly~j�e?jky��h)g°�Zosu°cfe?�lu{okq.h�bdo%rA}losnlo%osbdjsqdy{�ly~qpjsh)z|h¸ ¸ ¢¸ ¸�x»¸ ¸£�¤)¡ £¥¤?¡nlh?glnlo ¸>osb5osu`jkh)gM·d}l��e1nlh�q.o�e1u`nlo(¸8�²©e�ÄÅ}lgljsy��h)g�nlo�e?zUrAu{y~Álj�e?jky��h)gUosb¯·tL%4vDr&£Âo°%<� �q �q � £tУexA¸ %�v q ì £ex»¸�% ¢t ¸�x»¸~vo% £�x ¸�%�ð ì ££�ð z��}lo*nlokb.rl}8�okb�nlo*h)r�osq.e?qpn3e�u{}l�)e?qpe¯·tL%4vZr £Zo¿tm£�x�¡{¸�vR%eo¿t�¸1q�x�¡{¸�oÔ£°)¡4vo%{qtУex»¸�%�v q r £Do¿tm£�x�¡{¸�vR%eo¿tУ°{×±x»¸�vR%{qtУ�x»¸ %�v q  a�bdcfe�ÄÅ}Agljsy��h)g�z|osqdh)z|h)qdÄ e�c.y{osgAo%bd} �}lgly~jsh�r�h)u{h�okg<osu©bdosz|y{rlu{e?glh�nlokq.osji¦AhJtÅ��okbdc3�ee?jkh?cie1n3e�okg>osu:y{Ãk�K}Ay{osqdnlh�vÑ��»Bh)q�oku8rAq.y{gAjsy{rAy{h�nlosu:z��eMµZy{z|h�bdosq3�e O x5osbdcfe?�lu~o�b.yO�bl�h)u{h�bdyBrle?qfe�cfhKnlh0�s¦d§

�¼£Do¿tm£�x�¡{¸�voD��üoÈt�¸Ûx�£°*×�vy� q ��ß��¼£�x»¸�D���� q  î�¡

Page 91: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

a�u{o�±1e?glnlh|e?u`jk}3e?nlq.e?nlh�osg�e?z���h)bpz|y{osz��lq.h)b£DoË¡ �̸Ûx £× � � q o �̸�x £× � q �n"~o¿tУexÊ¡{¸~v q � q ß�£Do�¡*¸ q � q oP¸["��n" 

­<�h?cfokb.oO��}lo8¡t�¸Âx�£°{×�v¡o?tУ�x�¡{¸�v q r ¡{¸ q o?tY¡{¸ q xx¡{¸No�£°{×�vNr ¡*¸ q �¥jsh?g�u~hpjs}3e?u?u{h)bcZ�osq.z|y{gAh)b�osgh�yq�b.o5b.y~zUrAu{y~Álj�e?g���u{e%nlokb.y~�)}3e?u~n3e?n�b.o5q.oknl}ljso�e¥t�¸0x´£�°{×�v�q�� " ß�¸ " � "��}lo*osbÉcfqdy~±Kywe1u{z|osg�cfo]jsy{okqdcfe�r�h)qd�K}Ao¥t�¸�x�£°{×�vyq æ ¢*m¤× æ ¸ " �ö°ë~ü`ë ê��©ë e�vpºZo*rl}Aosnlo%b.}lr�h)glokq�tÅnly~±Ky~nly{okglnlh�r�h)qp}lg3e�jsh)gAbdcie1g�c.o�vÈ��}lo�´¥t ¢�vNrµ?tY¢�vDrÿ£?��nAo�z|hZnlh|��}lo�c.hZnAh�u{h|��}lo�¦le��Ç��}lo�¦3e?jsokq�okb�¦3e?u~uwe?q��3�]¼��.@x�dë�cie?u~osb��}lo £Zoa�4�·oP¼�� q

£Zo°@Ð�0oPë4� q r £Do»��o � q¡ o � ÷Õ o � "¡1� oPÆ¥tL� � vР�]uPz�}luªcfy~rlu{y~j�e?q�okuPb.ok�)}lglnAh�zUy~osz��lqdh�r�h)qx£�o�@Ú�(o)ë4�Iq��Abdoxcfy~osglo1�Abfe1u~±)h�cZ�osqdzUy~glh)bÆ¥tL� � vÑ�

£ÂoÈtL@NoÔ£vy�0o¿t�ë3o°@No £¡ vÌ� q oÈt�ë3o £

¡ @No £Õ vÌ� ÷ oÈt £¡ ë3o £

Õ @No £¡1� vÌ� "  

�]b��� rl}lokb]¦le����K}Ao�qdosb.h?u~±)okqÉosu`b.y~bdc.oszUe�u~y{glose?u�0r�@No £ ¼ r¿ë±o°@No £

¡¢År¹ë±o £

¡ @No £Õ ¢ r £

¡ ë/o £Õ @No £

¡1�²©e�b.h)u~}ljsy��h)g&�}lgly{jse�osb/�0r�xM@�r £°)¡K�I¼òr¿ë0r £�°Z£¥¡Z�K��uwe�e?rlqdh�µAy~z�e1g�c.o�nlo�»Ge?n8�ojkh)q.qdosb.r�h)glnAy{osg�c.o%okb |~tL�]v�r £Do �]°)¡�o»�IqÄ°Z£¥¡

£exA�]°?¡eo � q °Z£¥¡  �Iv%»Âh)q%b.okq�nlo�nAh)b�o�cie?r3e1bs��¯·t}%�vÅr ´?tL%�v�°,µ?tL%�v*jsh)gd´Ø�ݵår^h?u{y{gAh)zUy~h)bxnlo�)q.e?nlh�z|osglh)qph�y~�)}3e?u°��}lo�¡Z�p� r�h)qpb.okqÉnlo*h)q.nlokg��¯·tL%4vZr&£Do�%/o %{q

¡ o % ÷Õ o % "¡1� oaÆwt}% � vÄ »Bh)qOuwex}lgly~jsy~n3e?n�nloÉuwe?b:e?rAq.h�µZy{zUe?g�cfosb�nAo]»Âe?n8�o1�!¯·t}%�vOokbOuwexÄÅ}lgljky��h)g�nloku�e?r3e?qmcie?nlhe?g�c.osq.y~h)qs�Á j�v�ºZos���}Ag³oku:q.e?Ãsh?g3e?z|y{osg�c.h�e1g�c.osqdy{h)qk�Âokg"osbmcie?b�jsh)gAnly{jky{h)glokbs��¯·tL%�v�nlok�^oUb.osqu{e�e?rlq.h�µZy{zUe?g�cfo�nAo<»Âe?n8�o�tiE4z�Ev�nlo�uwe#oѵAr�h)glokgljsy{e?uÏ��»�q.hKjsoknly{okglnlh´jsh)z|h'osg�osu

î4×

Page 92: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

rlqdy{z|osq�e?r3e?qmcie?nlhA�vu{h)b�jshKokÁ3jky{okg�c.osb�nlo��okbdcie#bdo�rl}loknlosg\j�e1u{js}Auwe?q�jsh)z|h#b.h?u{}ljky��h)gnlo�}Ag´bdy{bmcfoszUe�u{y~glo�e1uÂjkh)zUrle1cfy~�lu{o�nlokc.osq.z|y{gle?nlh\t r�h)qxu{e�o�µZy{bmcfokgljsy{e���}lgly~jsy{nle?nIvjkh)g"jkhZo�Á3jsy~osg�cfokb�qfe1jsy{h?g3e?u{okbs�U»Âh)q%uwe�q.ok�)uwe�nlo�¬�qfe1zUokqs�Buwe�b.h)u~}ljsy��h)g�cie?z��Ay��osg´osbq.e?jsy~h)g3e?uY�ÌÎÍ ö°ë{ü°ë ên�°ë tÏÓxz|y~cfy~nlh�vÑ�Q�Ü R CTS�à < à�ç�UVCsé�äXWÊç\C�áOé�äü°ë ê�ë ê3ë ºZose]ÂÑ�Buwe�e1rlq.h�µZy{zUe?jsy��h)g�nlo}å1tL����v��3jsh?gÇu{e�glh?cie1jsy��h?g�¦3e?�lyªcf}3e?uu�0r¹�I���¼òr�É?½]��¯¥rÙt�¼�x.�nv¡°Tû´��Æxosu«djkhZjky{osg�c.o�y{gAjsq.okzUokg�cie?u~¯]r3e1qfe]u{e5nAosq.yª±1e?n3e]bdos�)}Agln3eA�bdo*c.y{okglo ÂÑ��� � o�ÂÑ� � � x\¡¢ÂÑ�¯ q rp|~t����LvÐz D1r�£4zÑ¡nzj j j �û x+£)¸

nlh?glnloxbdo�nlokÁ3gAo?�3jsh?zUh�okbpg3e1c.}lqfe?uY��Â1�sr Â�½»r ¢A��a�bmcfh�b.o�rl}Aosnlo�okb.jsqdy{�ly~q�jkh)zUhoku`b.y{bmcfokz�e�jsh?g�zUe1cfqdy{Ã5cfq.y~nlywe1�)h)g3e?u

¯�� q ÊËËËËËÌxx¡ ££ xx¡ £� � � � � � � � �£ x�¡ ££ xx¡

Í ÎÎÎÎÎÏ ÊËËËËËÌ � q���Â�½ � qÂ�½ � �

Í ÎÎÎÎÎÏ r ÊËËËËËÌ|~tL� � v|~tL� q v���|�tL� ½ � q v|�tL� ½ � � v

Í ÎÎÎÎÎϺZose��)½ � � u{e\zUe1c.q.y{Ã<nlo³jkhZo�Á3jsy~osg�cfokb�nAo³okbdcfo´b.y~bdc.oszUe\bdy{g osu�Ä e?j�cfh)q¶¯ � q �Æxokbfe?qdq.h)u~uwe?glnAh�r^h?qpuwe�rlq.y~zUokqfe�jkh)u{}lz|g3e�bdo*c.y{okglo

nAokc~�)½ � � r�x�¡*nAokcm�)½ � q xÊnlo�cm��½ �n÷  »Âe?qdc.y{osgAnlh�nloxu~h)bO±?e1u{h)qdosb�y~gly{jkywe?u~osbOnlo�cm� � r�x�¡Z�Znlokc~� q rÈ×A�Zglh�osb�nly~Äm�� jsy{u3rAq.h1��3e1qpr^h)qpy~glnl}ljkjsy��h)g�nlokc~�)½ � � rÙtyx�£�v ½ � � û´�:»Âh)qpcie1g�c.h�nlokc O r�t�x3¯ � q v ½ � � û³�

ü°ë ê�ë~ö°ë tY¬��©��h)qdosglh�rP�K¡)¡4ï4vÑ�*­]}lz|osq.e?glnlh�u~h)b�jky{gljkh�glhZnAh)bxy{g�c.osq.y~h)q.okbxnlo�y~Ã����}ly~osq.nle�e�nlokq.osji¦leÇ��nloUe?qdq.y{�le�e�e?�le¥·dhl¸©�'e?rlu~y{j�e1glnlh�osg´j�e1n3eÇ}Aglh�nAo|oku{u~h)b�uweÄ1�h)qdz�}lu{e�nlo%u{h)bÈjky{gljkhUrA}lg�cfh)bk�3b.o%h)�Acfy~osglo�oku`b.y~bdcfokz�e q oé " o\�(x"�  � r ¢7z  � o� ÷ o�¡±x>�  q r ¢Hz  q oP×VxÊ�  ÷ r ¢Hz � oé � oË¡Vx"�  " r ¢7z  " oP×VxÊ�  � r ¢H î?�

Page 93: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

®Éosbdh)u~±Ky��okglnlh)u~hl�Abdo*u{u{ok��e�e�uwe�b.h?u{}ljky��h)gtn � zp q zp ÷ z� " vNr £

¡?Õ tÅ�l£4zÚ×)¢7zÑ¡4ï7zÚ×?¢HzÑ¡4ï4vР»Bh)qxuweUb.y{z|okc.q��� e|nlokuvrlqdh)�lu{okz�e|b.o�rl}Aosnlo�e?g�c.y{jsy~r3e?q³Â q rá " �Ý ÷ rá � �°u{h���}lobdy{z|rlu{yªÁ3j�e�u{e�q.okb.h)u~}ljsy��h)g�nlosu`bdy{bdc.oszUeA�ºZose ¤ÂÑ�Âuwe�b.h)u~}ljsy��h)g�js}3e1glnlh|b.o%y{gljkq.osz|osg�cfe?g�u~h)bp±1e?u{h)qdosbpnlo%jsh?g�c.h)q.gAhUokg�}lglez|y{u��osb.y~z�eZ�°osg�cfh?gljsokb Ä > � t ¤Âpxc±v.r ¢A�Âjkh)gét ¤ÂÝxc±v ùù Ç�ä rÞ¢*m ¢)¢A£|osg"c.hZnAh)b*u{h)bglhKnlh)bk��²©e�bdh)u{}ljky��h)g�nAo�osbdc.o�b.y~bdcfokz�e�okb�h)��±Kywe?z|osg�cfo ¤ÂÈx�Â�r�¢*m ¢)¢A£?�Posb*nlokjsy~qs�¤ÂÈr ÂaoË¢#m ¢)¢A£)�

ü°ë ê�ë~ü°ë ¬�h)g´uwe�g�}lz|osq.e?jsy��h)g'y{glnAy{j�e1n3eA�°oku�D¡x��osbdy{z|hÇgAhZnlh�glh�okbdc��eÇe?uvu{e?nlh�nlou{e�ÄÅqdh)g�cfokqfe�bdy DhÃr t�û x £vy¢pt ÄÅq.h)g�cfokqfe�nlosqdosji¦3e4v���D?Ãr £eo�t�û x £vy¢pt ÄÅq.h)g�c.osqfey~Ãs��}ly{okq.n3e4v��1D/æ Ü £4z�ûãxU£6Þüt ÄÅq.h)g�cfokqfe5b.}lr�osqdy{h)q�v©o D/æ t¡t�ûPxU£v q xwt�ûãx|£vÄzt�ûãx|£v q Þt ÄÅq.h)g�cfokqfe�y~gAÄÅosqdy{h)q�v��*a�g'osb.o�jse?b.h�uweUosjs}le?jsy��h)g D¡x��osb.y~z�e�qdosbd}lu~cfe?g�cfo�e?uGe?rlu{y~j�e?q]uweÄ1�h)qdz�}lu{e�nlo%u{h)bÈjky{gljkhUrA}lg�cfh)bÉosbx/û q tnÂÑ� � � o�ÂÑ��� � o�ÂÑ� � ß ½ � � � o�ÂÑ��� ß ½ � � � xÊ� ÂÑ�Lv�rÈ|Z��z�)e|��}lo*rlqdh¥±Ky~osglo%nlosu`okb.��}lokz�e

� A �2q ø � �sr� A � � � A � A � �

� A �Vq ø � �sra�bdc.h<��}ly{okq.o|nlosjky{q%��}loUrle?qfe�u{h)b³D5jsh)gAb.y{nAosqfe1nlh)bs�Âb.y O r`t�� â A v�osb%uwe�zUe1cfqdy{Ã�l}Ab.j�e1n3eA� �C����rÔ��û q z �C��� � � rÈ�C����� � r¿� ��� � ß ½ � � � r¿� ���Þ� ß ½ � � � r�x/û q  

²`h���}lo�bdo%e¥·d}lbdcfeUe�u{e�ÄÅh?q.zUe�y{glnly~j�e?nle�osgÇosu`osg�}lgAjsywe1nlhl���uPjsh)glbdy{nlokqfe?qpoku`q.okbdcfh�nlo�u~h)bȱ1e?u{h?q.osb�nlo³Dv��e?rlu~y{jse?q�u{e�Ä1�h)q.z�}Auwe�nlo*u~h)bÈjsy~gljshrl}Ag�c.h)bs�©r�h)qxu{e�jsh)glnAy{jsy��h)g�å ùù Ç�ä r ¢A�`uwe �}Agly{jse�nly~ÄÅokq.osgAjsywe�okb*�K}Ao�u{h)b�glhKnlh)b���}lojse?osg�osg|uwe5ÄÅq.h)g�cfokqfe�glh%e?r3e1q.osjkosg°�v­]h*osbOnlyªÄm�� jsy~u�jsh)g�±)okgljsokq.bdo�nloÉ��}lo��osbmcfh)b�jkh)q.qdosbm�r�h)glnlokg#e|u{h)b5jsokq.h)b5osg�cfqdo�u{h?b5�Au{hK�K}Aosb5�K}Ao�jsh?zUr�h)glokg<uwe�zUe1cfqdy{Ã�h�e|u{h)bÉuÏ�� z|y~cfokbnloÊ�osbmcieA�U¶Oo�e?z|h)b*nlh)b%oзdokzUrlu~h)b?tÅÄÅqdh)g�cfosq.e?b*b.}lr�osqdy{h)q*�'nlokq.osji¦le�v��Âu{h)b*h?c.q.h)b*nlh)bbdh)g�jkh)z|rlu{o�cie?z|osg�cfoxe?gÉ�e?u~h)�)h)bk�î�à

Page 94: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

²`h)blD�jsh)g £ æ D æ ûix £#osbmc��e?g+okg�uwe�ÄÅq.h)g�c.osqfe³b.}lr�osqdy{h)q|�Ëu{e³okjs}3e?jky��h)ge?bdhZjkywe?nle�e|oku{u{h?bÈosb x/û q t�Â�� � � oéÂ��Þ� � oéÂ��Þ� ß ½ � � � xÊ� ÂÑ�Lv�r¿|3�Ì a�uÂcZ�osqdzUy~glh�e?}Ab.osg�c.o�jsh)g�qdosb.r�osj�cfhÇe?uBj�e?bdh�e?g�cfokq.y{h?qs�ÑÂÑ� � ß ½ � � � �Pbdy{z|rlu{okzUokg�cfo�y~gZ�nly~j�e���}lo*uwe�zUe1cfqdy{Ãxjkh)z|y{osgAÃ�e�osgÇuwe�jkh)u{}AzUg3e�£?�lzUy~osg�cfq.e?bp��}lo³Düx¹t�û x+£�v æ ¢A�»Bh)qxh?c.q.h�u{e?nlhl�^u{h)bMDpjsh)g¥DÂr t�ûêx £�v�¢G�G£ æ ¢ æ ûêx £)�Posbdc3�e?g�osg'u{eUÄÅq.h)g�c.osqfenlokq.okji¦3e|��u{e�osjk}3e?jsy��h)gÇjsh)qdq.osbdr^h?glnly{okg�cfo*osbx3û q t�ÂÑ� � � o5 � � ß ½ � � � o� ��� ß ½ � � � x"� ÂÑ��vNrp|Z�Ç a�upcZ�okq.z|y{glh³e?}lbd}losg�cfo<osbdcfe³±)okÃ?�rÂÑ��� � �pokb�q.okb.r�h)glb.e?�lu{o�nloÇuwe"e1gK}Auwe?jky��h)g�nloÇu{h)boku{osz|osg�c.h)b0�C����� � jk}3e?glnlh¥D(rùt�ûXx�£vy¢G�p£ æ ¢ æ ûXx&£)�'a�bdcfh?b�jsokq.h)b�okbdc��e1gbdy~cf}le?nlh)bpokg�u{e�rle?qdc.o�y{gAÄÅokq.y{h?qÈnlosqdosji¦3e|nlo*j�e?nle|�lu~hZ��}lorw%�ü°ë ê�ë¤�©ë e�vÈ�5g�bdosgljky{u~u{h�j`�e1u{js}Au{h�rlqd}los�3eÄ $ � ¿ r�x � qñ tL¢ q o°� q v $ � ¿  

ÆxoxÄÅh)qdz�e���}lo1��b.}lr�h)gly~osglnlh|uwe�jkh)g�±)okq.�)okgljsy{eA� Ä å�o « åâr ¢|y~zUrlu~y{jse0B¿ Ð �32 � � � ¿ � « x � qñ t�¢ q ov� q v � $ � ¿ r ¢H »Bh)q�uwe�}lgAy{jsy~n3e?n�nlo�u{e�q.okrlq.okb.osg�cfe?jsy��h)g°�1� � ¿ t « x � q t�¢ q o�� q v�°{ñ�v/rÿ¢Z��ºZy « æ¡ � qа{ñ<okg�c.h)gljkosb « x � qt�¢]qso��âqÄv¡°{ñ æ ¢<�>glokjsosb.e?q.y{e?z|osg�cfoâ� � ¿ r�¢A��r^h?q�u{h��}lohå r ¢A��»Bh)q*h?cfqdh�u{e?nlhl�©r3e?q.eÇjk}3e?u~�K}Ay{osq}� ¦a§��1� $ �Ì� okb�bdh)u{}Ajsy��h?g´jk}3e?glnAh« r ¡ � qа{ñZ��Iv%¬�h)g>u{eÇglh1cie?jky��h)g´nlosu:rlqdh)�lu{okz�eÇe?g�cfokq.y~h)qs�Bjsh)g)û r ×A�©cfhKnlh�u{hÇ�K}Ao�¦3e����}lo5¦3e?jkosq�okb8¦le?u{u{e?q�osu�z|osglh)q « r3e1qfe�oku��K}Ao]oku^bdy{�)}ly~osg�cfoÉbdy{bdc.oszUe*c.osgl�)e�y{gZÁ3gly~cfe?bbdh)u{}ljky{h)gAosb(t oku°Ä e?jkc.h)qpo�µKc.qfe�£°{× q b.o%nlok�^o%e���}lo<µ�okb.Ü ¢Hz�×*Þ q ��gAh�Ü ¢Hz�£TÞ q vÑ�

£× q ñ ì w �� w ð \Âao « \¿r \¢H a�u « �l}Ab.j�e1nlh�bdosq3�eZ�3r^h)qÈcfe?g�cfhl�Aosu`zUe��?h)q5e?}Ac.h¥±1e?u~h)qÈnlo

x ì w �� w ð r ÊËËÌ � x%£ x�£ ¢x%£ � ¢ x�£x%£ ¢ � x�£¢ x%£ x�£ �

Í�ÎÎÏî)Õ

Page 95: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

��}lo�nAosb.rA}��osb�nlo�¦3e?jsokqxu{h?b]j°�e?u{jk}lu{h)b5osb « r�¡Z��a�uÂqdosb.}Au~cie1nlh�glh�okbdc3�e�nloszUe?b.y{e?nlhu~oзdh)bvnAo5¡ � q °{ñ.r ¡ m £�ñ4×ò j T v��}loÉb.oph)�Ac.osg°�� exosg|osulrAq.h)�lu~oszUe�y{gAy{jsy{e?uKb.y{g�e1rlq.h�µZy{zUe?qr�h)qpnlyªÄÅosq.okgljsy{e?bÈÁ3glyªcie?bk�ü°ë ê�ëÍ�°ë ¬�h)zUh�uweUgAh)q.zUe?u©osg�u{eUÄÅq.h)g�c.osqfeUnlosqdosji¦3e�e?rl}Ag�cfe�osg�u{eUnly~q.okjsjsy��h)g#nlo�©�3bdo%jk}lz|rlu{o Ç�ÒÇ�Ó r Ç�ÒÇ � �ºZose ÂÑ� ¬ uwe�e?rlqdh�µAy~z�e1jsy��h?g r^h?q�nly~ÄÅokq.osgAjsywe1b#Á3gly~cfe?b�osg&oku�glhZnAhÙt�����z�l ¬ v�rt�DÌ°{×Hz�N7°*×�v�� D�r�£4zÑ¡7zÚ×Z¸CN0r&£4zÑ¡Z�a�g>u{h?b�glhKnlh)b�y{g�cfokq.y~h)q.okbwt�� � z�l � vÑ�òt�� � z�l q vÑ�òt�� q z�l � v���t�� q z�l q v��vu{e�Ä1�h)qdz�}lu{eÇnlou~h)bpjsy~gljsh�rl}lg�c.h)b]jkh)glnl}Ajso%e|u{e?bposjk}3e?jky{h)glokb ��q o� q¡� xÊ�  �Ì� z  �Ì� o� ÷ � o� qÌq x>�  q¡� r ¢Hz �Ì� o� qÌq xÊ�  ��q z  ��q o� ÷ q o� q¡� x>�  qÌq r ¢H 

§�e?uªcie?g³nlh)b�okjs}3e?jky{h)gAosb�r3e?q.e<r�hZnlokq�cfokglosq�}lg\b.y{bmcfokz�e<nAokcfokq.z|y{g3e1nlhl� �a�bdcfe?b�b.orl}Aosnlokg h)�Ac.osglokq<e?rAq.h�µZy{zUe?glnlh\r�h)q�osu*jshKjsy~osg�cfo´y{gljkq.okzUokg�cfe?u�uwe\jsh?glnly{jky��h)gÔnloÄÅqdh)g�cfosq.e Ç�ÒÇ � r�x%£�okgAt�� ÷ z�l � v8�JtL� ÷ z�l q v��O²`h���}lo�nle�u~}l��e?qÉe ÷ � x� q¡�£°{× r�x%£4z  ÷ q x� qÌq£°{× r�x%£4 ®Éosbdh)u~±Ky{okglnlh#oku�bdy{bdc.oszUe�h)�ZcfosgAy{nlh»tÅu{h�js}3e?u8rl}loknlo�b.y~zUrlu~y~Á3jse?q.bdoUnAq3�e?bmcfy{jse?z|osg�cfo}lb.e?glnlh|uwe�bdy{z|okc.q��� e�nAosu`rlqdh)�lu{okz�e�jkh)gljku{}A�?osglnlhaÂÑ� � r Â�� q v��lbdo%u~u{ok��e�etn �Ì� zp ��q zp q¡� zp qÌq zp ÷ � zp ÷ q vNr�x £

£à tУ4z�£4zÚ×7zÚ×HzÚîHz�î�vÄ ü°ë ê�ëÍ�°ë e�vpºKo*c.y{okglo*u{h)bpnlokbfe?qdq.h)u~u{h)b�nlo*�Ge��Ku{h)q

|~tL��oã¯Iv�rp|~t��]vüoã| m tL�]v�¯�o |Im m�tL�]v¡ ¯ q o | m m m�tL�]vÕ ¯÷�oPÆ¥tǯ!"Äv|~t��¥x»¯Iv�rp|~t��]v�xa| m t��]v¡¯.o | m m�tL�]v

¡ ¯ q x | m m mLtL�]vÕ ¯ ÷ oaÆwtǯ " v»Bh)qpcie?g�cfh |~t��·oã¯IvüoP|~tL�?xa¯Iv�x�¡4|~tL�]v¯ q r¿| m m t��]vüoPÆ¥tǯ q vÄ �&nAo�e?��}`�� okbÈÄ1�e?jsy~u^h?�Acfokglosq Ä � å�x Ä å�r¹Æwtǯ q v8e?rlq.h�µZy{zUe?glnAh�jsh?g�osbdcfe�Ä1�h)q.z�}luwejse?n3e�}lg3e�nlo*uwe?bprle?q.jkywe?u~osbpb.ok�)}lglnle?bs�

î�ï

Page 96: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

Á �Iv�»�qdhZjkosnly~osglnlhÊjkh)z|h>osg�oku�e?rle?qdcfe?nlhÊe?g�c.osq.y~h)q�r�osqdhÊe?¦lh?qfe"jkh)g¹|~tL�]vdrå1tL��z¡l{�ÚvÑ�3b.o�cfy~osglo|�tL�I�1oã¯Iv�oã|~t��I��xa¯ v�r ¡*å0o ÆIqÚåÆ�� q ¯ q o £

£¥¡Æ " åÆ�� " ¯ " oPÆ¥tǯ � v

nlh?glnloÂå��%b.}Abvnlosqdy~±1e?n3e1bÂokbdc��e1g�ok±1e?u{}le?n3e?bBosg�t��I��z�l{�Úv��v»�qdhZjkosnly~osglnlh�nlo�u{e]z|y{b.zUeÄÅh)qdz�e5jsh)gh|�t�lHvNr¹å1tL�I��z�lHv��1b.oÈu~u{ok��e�ex��}loÈu{e�jsh?g�c.q.y~�l}ljsy��h)g�nlo�u{h)bvrA}lg�cfh)bvz|osnAy{h)bnlo*u~h)bpuwe?nAh)bposgÇosu`okb.��}loszUe�js}3e?nAqfe?nlh|nlo*uwe�Ál�)}lqfe�osb� � å1tL�I��oã¯uz�l*�Ðvüoaå1tL�I��xa¯uz�l*�Ðvüoaå1tL�I�Tz�l{�1oã¯Ivüo»å�t��I�jz�l*��oP¯Iv �r £�Õ{åÅo�� Ä å]¯ q o £× � Æ " åÆ� " o Æ " åÆ�l " � ¯!"~oPÆ¥tǯ � vÄ �]u`jsh)glbdy{nlokqfe?qe|�tǯIv�r¹å1tL�I��oã¯uz�l*��oP¯Iv�b.o*cfy{okglo?�|~t�¯Iv#o¥|~t�x3¯IvNr ¡*å�o B r3e?q.j1�Ob.os�?}lgln3e?b¯ q o £

£¥¡ B r3e?q.j1��js}3e1qdcie1bs¯!"4o¥Æwt�¯ � vÄ ��e?u^jkh)glbdy{nlokqfe?q�|�tǯIvNrÈå1tL�I�]oA¯uz�l*��x\¯IvÑ�Ab.o�h)�Acfy~osglo]osu^zUy~b.z|h�qdosb.}Au~cie1nlh�bfe1u~±)h��}lo�u{e?b�r3e1q.jsy{e?u{okb�bdos�)}lgAn3e?bÉjsqd}lÃ�e?nle?bÈcfokglnlq3�e1gÇ}Ag�b.y{�?glh�z|osglh)bk�A�Uuwe?bÈnAosq.yª±1e?n3e?bjk}3e?qdcfe?b�cfe?z��ly��osg´cfosgAnlq3�e?g"osbdc.o�bdy{�)glh�osg>oku8jse?b.h<osgÊ��}lo�bdo�nlokq.y~±?o�}lg"gx�}lzUokq.hy~zUr3e1q5nAo�±)okjsosb*jkh)g#q.okb.r�osj�cfh�e�jse?n3e�±1e?q.y{e?�lu~o¥tÅosbxnAosjsy~qs�^}lg3eU±?osÃ�jsh?g�q.osbdr^okjkc.he�}lg3e��#c.q.okb*±?osjkosb�jkh)g´q.osbdr^okjkc.h<e�uwe�h?c.qfe�vÑ���Bosgly~osglnlhÇosg´js}Aosg�cie�cfhKnlh)b*osbmcfh)bbdy{�)glh?bÈ��b.}lzUe?glnAhUoku°q.okb.}luªcie?nlhUe�uwe�okjs}3e?jky��h)g�e?g�cfokq.y~h)qpb.o*u{u~os��e�eå�t��I�~oP¯uz�l{�1oã¯Iv�oVå1t��I�Zxa¯uz�l*��x»¯Iv�o»å1tL�I�1oã¯uz�l*�Zxa¯Ivüo»å�t��I��xa¯üz¡l{�1oã¯Ivr �4åÅo�¡ Ä å]¯ q o £

Õ � Æ " åÆ� " o Æ " åÆ�l " oËÕ Æ " åÆ�� q Æ�l q � ¯ " oaÆwtǯ � vР��okbdcfh|osb5uwe�jkh)g�cfqdy{�l}ljky��h)g�nlo*u~h)bȱO�osqdc.y{jkosb5nlosu`okb.��}loszUe�nlo*uwe�Á3�)}lq.eA�ºZ}lzUe?glnAh�c.hZnle?bÉuwe?bÈjkh)g�cfqdy{�l}ljky{h)gAosbÉb.o*cfy~osglo���}loÕ�¯ q Ä_Ü åâr�x\¡?¢{å�o £�Õ*å�o\� Ä å�¯ q o £× � Æ " åÆ� " o Æ " åÆ�l " � ¯#"o��4åÅo�¡ Ä å]¯ q o £

Õ � Æ " åÆ� " o Æ " åÆ�l " oËÕ Æ " åÆ�� q Æ�l q � ¯!"NoaÆwtǯ � vr�Õ Ä å]¯ q o £¡ � Æ " åÆ� " o Æ " åÆ�l " o�¡ Æ " åÆ�� q Æ�l q � ¯#"~oPÆ¥tǯ � vР

î4î

Page 97: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�a�bdc.o�osb*osuvqdosbd}lu~cfe?nlh��l}lbdj�e?nlh���e���}lo Ä t Ä å]v�osb*uwe�jkh)z��ly~g3e?jky��h)g#nAo|nAosq.yª±1e?n3e?bjk}3e?qdcfe?bÉ��}lo%e?r3e?qdosjso%osgÇosu`rle?qK�okg�c.osbdy{bs�j�v*ºZyNå´osb%b.h?u{}ljky��h)g�nlo Ä å?o « å�r ¢�okg�c.h)gljkosb Ä t Ä å�v3r²x « Ä å©�`��r�h)q�osue?rle?qdcfe?nlh|e?g�cfokq.y{h?q Ä_Ü å¥x Ä åâr ¯q£¥¡ tyx « v Ä å�oPÆwt�¯!"ÄvÄ 

ºZ}Abdcfyªcf}A�?osglnAhUcie1z��ly��okg Ä å�r�x « å©�3bdo*c.y{okglo*uwe�y{�?}3e?u{nle?n�osbdr^okqfe?n3eZ�ü°ë ê�ë � ë a�u©nlosb.e?q.qdh)u{u~h|nAo��Âe��Zu~h)qɦ3e?bmcie�h)q.nlokg�¡�nloÅ|~tL�0oã¯Ivp�d|�tL�wxa¯IvÈjsh?gcZ�osq.z|y{gAh�nlo*osq.qdh)qs�3y~zUrAu{y{jse|~t��0oP¯ vüoP|~tL�?xa¯Iv�x�¡4|~t��]vNrp| m m tL�]v¡¯ q oPÆ¥tǯ÷�b.}lr0� | m m m � vÄz

nlo*z|hZnAh��K}Ao�r3e1qfe�r^h?u{y{gAh)zUy~h)b:nlo*b.os�?}lglnlh|�)qfe1nlhl�ljk}3e?u{��}ly~osq.e���}lo%b.ose¥¯|~t��0oP¯ vüoP|~tL�¥x»¯Iv�x�¡4|~t��]v¯ q rp| m m tL�]vÄ ¬�h)gAb.osjk}losg�c.osz|osg�cfo|r3e?q.ewå�t���z�lHver t���xa�IqÄv6t�l·xal7qÐvÑ�°��}lo�osb�}Ag´r�h)u~y{glh)z|y{h�nlobdos�)}lgAnlh��)qfe1nlh�osg�jse?n3e�±1e?qdywe?�Au{o?��u{e%Ä1�h)qdz�}luwe%nloxu~h)b8jky{gljkh�rl}lg�cfh?bÈosbÈoѵAe?jkcfeA����u±?osq.yªÁ3j�e1q.b.o Ä > � ådr Ä å�osg<u{h)b5glhKnlh)bs��uwe�b.h?u{}ljky��h)g�q.o�e1uBjkh)y{gAjsy{nAo�okg#osu~u{h)bÉjsh?g#uweh)�ZcfosgAy{n3e�e?u`e1rlu{y~j�e?qÈoku`osbd�K}AoszUe|nlo*nlyªÄÅosqdosgljkywe?bpÁ3glyªcie?bk�ºZy©a�q.qdh)q ¡ �±°Tû?É%osg�cfh?gljsokb]u~h)�:aOqdq.h)q ¡ u~h)�Z�Èx Ê u{h?��û³�3nlo�zUe?glokqfe���}lo*u{h)bu~h)��e?qdy~cfz|h)bBnloÉu{h)bv±1e?u~h)q.okb�nloÉuwe�cfe?�luwe�bdo5nAos��osgUe¥·d}lbdcfe?q:e�}lg3e*q.osj�cie*nloÉr^okglnly~osgZ�c.oÅx Ê �O�]glh�rl}loknloxjsh?glb.ok�)}ly{q8zUoE·dh)q.okb8qdosbd}lu~cfe?nlh)b8}lbfe?gAnlh�q.ok�)q.okb.y��h)g�u{y~glo�e1uÏ��r�osq.h}lgle|e1rlq.h�µZy{zUe?jsy��h)g�osb

x Ê r Ä lÄ � r u{h)��tm£ m ¢)¢?�V��£�¢ �n÷ v�xÊu{h)�ItУ m ×Z£¥¡3��£�¢ �n÷ vu~h)��ñVxÊu{h)��î r�xx¡ m ¡4ïs j j ��}lo*b.}A�)y{okq.o*��}lo�oku`h)q.nAosgÇosb]¡Z�

� ü°ë ê3ë� Æxosbfe1q.q.h?u{uwe1glnlh�r�h)qp�Âe��Ku~h)qposg)tL���Ìz¡l ¬ vå�t������ �*� ¿ z�l ¬ vNrÈå1tL���7o¿tL¢âxd�¶v¡¯uz�l ¬ v�r q � � �B â 2 � £� { Æ â åÆ� â t�¢�x��¶v â ¯ â oPÆwt�¯ q � � q vР»�q.hKjsoknly{okglnlh�nlo´uweÊzUy~b.zUe>z�e1glosq.e�jkh)gÈå1t����Ìz�l ¬ � �*� ¿ v��Ôbd}lbdc.y~cf}Z�)osgAnlh+osg uweÄ1�h)qdz�}lu{e#nlosuÉosg�}lgAjsywe1nlhl���le?bdcfe³rlqdh)�3e?q���}loÇr3e?qfe�cfhKn3e�ÄÅ}lgljky��h)gP|Ù¦��(q � � q�b.o

î4ñ

Page 98: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

jk}lzUrAu{o| ß q ����tL��v�r £¯ q � q �B¿ 2 � t�x%£v ¿ ì ¡*¢� ð q �

� �B â 2 � t�¢âxd�¶v â ¯ â� { | ß â ��tL��vР­<�h?cfokb.o���}loJtyx�£�v:¿<� q �¿ � t�¢�x��¶vyq � � �*cfh?z�e�±1e?u{h)qdosb�h)rl}lokbdcfh?b�js}3e1glnlh � r²Ø´�� r ¡*¢Vx�Ø��Zr�h)q�cie?g�c.h%u{e�jsh)g�cfqdy{�l}Ajsy��h?g|nAo5u~h)b�cZ�okq.z|y{glh)bGjsh)g�(r ¡*¢eo'£]okb8g�}lu{eA���u{e�y{nlokg�cfy{nle?nÇe?g�cfosqdy{h)qpok��}ly~±1e?u~o*eq �B¿ 2 � t�x%£v ¿ ì ¡*¢� ð tL¢¶x��¶v â� { r 6 ¢ b.y©¢·ß�� æ ¡*¢£ b.y��(r ¡*¢a�bdc.hxb.o8b.y~�)}lo:nlo�u{e5Ä1�h)qdz�}luwepnlo8uweÉy{glnAy{j�e1jsy��h?g�nlokq.yª±?e1glnlhG�p±?osjsokbs����e]�K}Ao�b.okgl¦?�Nr�uoPÆ¥tL� ÷ v�y~zUrlu~y{jse�b.okgl¦ q � �Nr¹� q � oaÆwtL� q � � q vÈnlo*zUhKnlh���}lo

ë âë4� â ùùùù ­ 2 � t b.okgl¦ q � ��vZr76 ¢ bdy©¢hß�� æ ¡*¢tÏ¡*¢uv�{ bdy��(r ¡*¢Á ü°ë ê�ëÍ& ¬�h)g�uwe?bÂnlokÁlgly{jky{h)glokb�y{glnAy{j�e1n3e?bGokb�jsh)z|hxbdyluwe�bdy{z\�okc.q.y{jse�nlopu{e]ÄÅq.h)g�c.osqfey~Ãs��}ly{okq.n3e�okbdcf}Z±Zy~osq.eUe�jsh?g�c.y{g�}3e?jky��h)g�nlo*u{e�nAosq.okji¦3eUh�±Ky{jkok±?osq.b.e

t � ½ � ¬t Â�½ � � ¬t � � ¬

t Â�½�½ � ¬uv

¾�osh)z\�okc.q.y{jse?z|osg�cfoÉosbmcie�bdy~c.}3e?jsy��h)g|b.o�rA}losnlo]q.okrlq.okb.osg�cfe?qÈosg�c.osglnly~osglnAh���}lo�okg±?osÃ�nlo�qdosb.h?u~±)okq�osu]rlq.h)�Au{oszUe"okg�}lgÔq.osj�c��e?gA�)}lu{hA�5bdo�osbmcie>q.okb.h)uª±Ky{osgAnlhÊosg�}lgle�3e1gln3e�nlo���fh)�ly~}lbs�¬�h)g�okbdcieUq.osrAq.osbdosg�cie1jsy��h?g�osg�z|osg�cfo1�Puwe|rlq.}Aos�3e�nlo�uwe|o�µZy{bmcfosgAjsywe|�<}lgAy{jsy~n3e?nbdos�)}ly~q3�e�uwe1bxzUy~b.zUe?bxuÏ�� glose?bx��}lo|osg´osuvjse?b.hÇnlo�}lg´q.osj�c��e?gA�)}lu{hA�`�)qfe?jkywe?bxe���}lo|b.ojk}lzUrAu{o%nlo�zUe?glosq.e�e?gÉ�e1u{h)��e�osuÂrlq.y~gljsy~rly{h|nlokuÂz��eMµZy{z|h�tÅuwe�Ä1�h)q.z�}AuweUnAo�u{h?b�jsy~gljshrl}Ag�c.h)b%r3e?qfe Ä å»r ¢�y{z|rlu~y{j�e���}lo|osu�±1e?u~h)q�osg³j�e?n3e�glhKnlhÇosb%rlq.h)z|osnAy{h�nlo|u{h)bnlo'u~h)b�e?u{qdosnloknlh)qdosb�jsh)gÔu{eÊc.h)r�h)u{h)�l�� e³nAo´u{eÊ�3e?gln3eÊnlo³��fh?�ly{}lb�v�� ²©e?b��}lgly~j�e?bÄÅqdh)g�cfosq.e?b���}lo'r^okq.bdy{bdc.osgÔb.h?g u{e?b�nlo'u{e"r3e?qmcfo�nlo´e?qdq.y{�le³��e?�le¥·dhl�É��e\�K}Ao�uwe?bÄÅqdh)g�cfosq.e�y{Ãs��}ly~osqdn3e���nlosqdosji¦3e|¦3e?gÇnlosb.e?r3e?qdosjky{nlhUe?u°y~nlosg�cfyªÁ3j�e1qs�ñ)¢

Page 99: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ü°ë ê�ë ê�+`ë ºZose ÂÑ� ¬ �`jsh?zUh�okb�¦3e?�lyªcf}3e?uY�°uwe�e?rlq.h�µZy{zUe?jky��h)g#�A}lb.jse?n3e�nlo0å1tL����z�� ¬ vjkh)gP���År D̯°�e¯¿r £°Tû³�Z� ¬ r NnØ^�+²Be1bUjkh)glnly~jsy{h?glosb|nloÇjsh)g�cfh?q.glh³b.o<rA}losnlokge?rAq.h�µZy{zUe?qÈjsh?zUhÂ�� �òr¿|�tL���LvÐz ÂÑ� � x�Â�� �Ø r�uut����LvÐz Â1� ¬ r Â�½ ¬ r ¢H »Bh)qÉh?cfq.e�rle?qdc.o?�lu{e�okjs}3e1jsy��h?gÇbdo�e1rlq.h�µZy{zUe�r^h?qÂ�� ¬ � � o�ÂÑ� ¬ � � x�¡ Â�� ¬Ø q r ÂÑ��� � ¬ oéÂ�� � � ¬ x�¡¢ÂÑ� ¬¯ q  ­<�h?cfokb.o���}loUuwe?b�jsh)glnAy{jsy~h)glokb�nlo�jsh)g�cfh?q.glh#nle?g>y{gAzUoknlywe1cfe?z|osg�cfo�u{h?b%±1e?u~h)q.okb�okgu{e?b�nlh?bÈrlq.y~zUokqfe?b�«mÁ3u{e?b.¯l��ÂÑ� �È�aÂ�� � ¸Az|y{osg�c.qfe?bÈ��}lo�uwe�okjs}3e?jky��h)g�r�osqdzUyªcfo5j�e?u~js}lu{e?qu~h)bp±?e1u{h)qdosbÉosg�uwe�Á3uwe�D]o £4x��osb.y~z�eZ�.Â��Þ� � ¬ ��osg�ÄÅ}lgljsy��h)gÇnlo�u~h)bɱ?e1u{h)qdosbÉosg�uwe?bÉnlh)bÁ3u{e?bÈe1g�c.osqdy{h)qdosbs�vÆxo�osbmcie�ÄÅh)qdz�eZ�KokuPz\�okc.hZnlh�nloxnlyªÄÅosqdosgljkywe?b:Á3gly~cfe?b�jkh)glnl}Ajso�e�}Agbdosgljky{u{u~h�z\�o�cfhKnlh�y~c.osq.e1cfyª±)hl�

ü°ë ê�ë ê�ê3ë »Âh?q5u{e�q.ok�)uwe�nlo*uwe�jse?nlokg3eA�3jsh?g¶�ârc�Gjkh)b�ãZ��l·r��Gb.okgGãK�lb.o%h)�Ac.y{okgloÆ�åÆ�� rÔjsh)bVã Æ�åÆ� o\b.osgMã Æ�åÆIl z ÆIåÆ�ã r�xH�vb.okgGã Æ�åÆ� ov�Gjsh?b�ã Æ�åÆ�l  Æxokb.r�oз.e?glnAhUokg�okbdcie1bÉÄ1�h?q.z�}lu{e?bs�Ar3e?qfe�jk}3e?u{��}ly~osqÈÄÅ}lgAjsy��h?g�òÆ�òÆ� r jsh)b�ã Æ�òÆ�� x bdosgMã� Æ�òÆ�ã z Æ�òÆ�l r bdosgMã Æ�òÆ�� o jkh)bVã� ÆIåÆ�ã  Æxo�z|hZnAh��K}Ao Æ�qÚåÆ� q r ÆÆ� ì jsh)b�ã Æ�åÆ�� x bdosgMã� ÆIåÆ�ã ð  �Écfy{u~y{Ãse?glnlh*nloxg�}lo�±)h�u{e%Ä1�h)qdz�}luwe*r3e?q.e�Æ�ò7°,Æ�<r�osqdh�e?¦lh)q.e�bd}lbdc.y~cf}Z�)osgAnlh�ò�r^h)q8uweÄÅ}lgAjsy��h?gÇokg�cfq.o%r3e?qK�osg�cfokb.y~bs�3b.o%h)�Ac.y{okglo�nlosbdrl}8�okb�nlo*h)r�osq.e?qÆ q åÆ� q r b.osg q ã Æ q åÆ�� q o jkh)b q ã� ÆIåÆ�� o b.osgMã'jsh)bVã� Æ q åÆ��,Æ�ã o jsh)b q ã� q Æ q åÆ�ã q x b.okg�tÏ¡,ã{v� q ÆIåÆ�ã  a�uGoE·do0�Þbdo�h)�Ac.y{osgAo�e�r3e?qmcfy~q�nlokuGoзdo�É zUoknlywe?g�c.o�}lg��)y~q.hUnlo��e?gl�)}Au{h � °)¡Z�Pr�h)qu~h"��}lo�uwe'Ä1�h)q.z�}luwe'r3e?q.edÆIqÚå]°,Æ�lnq�b.okq3�e>y~�)}3e?u5bfe?uª±)h>oku�jse?z��ly~h�ãwG ¾ ã0o � °)¡Z�ºZ}Az�e?gAnlh|e?z��3e?bpoѵZrlq.okb.y{h?glosb5b.o%u{u~os��e�e1u`q.osbd}lu~cfe?nlh�nlokb.o�e1nlhl�

ñA£

Page 100: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

��u�nly{bdjsq.o�cfy~Ã�e?q�nlo'u{e"z�e1glosq.e\y~glnly~j�e?n3eZ�5u~h)b�glhKnlh)b�bdosq3�e1g okg jkhZh?q.nlokg3e?n3e?br�h)uwe1q.osb(t��z�ã4vt}� � z�ã � vNr�t�×Hz � × vÐz t}� q z�ã q vZr�t�×Hz � Õ vÄz t}� ÷ z�ã ÷ vNr�tY¡7z � × vÐz t}� " z�ã " vZr�tÏ¡7z � Õ vÄ ºZose?g� � zp q z� ÷ z� " uwe?bUe?rlqdh�µAy~z�e1jsy{h?glosb�nlo�u{h)b�±1e?u~h)q.okbUnlo¶å�osgËosbmcfh)bUglhZnAh)bs�²©e?b�jsh?glnly{jky{h)gAosbÇnlo´ÄÅqdh)g�cfokqfe\y{z|rlu{y~j�e?géå1t �Hz�ã4v\r �l�±å1tm£4z�ã4v\r £)�Vå1t}�zi¢�v\rå1t}�z � °)¡4v~rc�K�OÆxo�zUe?glosq.e��K}AoÆ�qÚåÆ�� q t}� � z�ã � v ¡ å1t �z�ã � vüoaå1t}� ÷ z�ã ÷ v�x�¡*å1t}� � z�ã � v£ q ¡ �/o� ÷ x�¡¢Â �  ��nlo*u{e�z|y{bdz�e%ÄÅh)q.zUeA�

£� q� Æ q åÆ�ã q t}� � z�ã � v ¡  q oa×}xÊ¡¢Â �× q t � °{×�v q z £� � Æ�åÆ�� t�� � z�ã � v ¡ �Vx� �×V��£  ²©e�osjk}3e?jsy��h)gÇq.osbd}lu~cfe?g�cfo*osb

�/o� ÷ x�¡¢Â � o �}x� �× o  q oP×Vx�¡¢Â �� q °*× r ¢H �]gÉ�e?u{h?��e?z|osg�cfo1�Aosg)t}� ÷ z�ã ÷ vÈb.o*h)�Ac.y{okglo

£Âoé � x�¡  ÷ o  � x� ÷¡ o ¡�o� " xÊ¡¢Â ÷¡ q � q °{× q r ¢7 »Bh)q�uwe�b.y{z|okc.q��� e�nlokuÈrlq.h?�lu{okz�e#eÇcfqfe�±��osb�nlo�uwe<�ly~b.okjkcfqdy{Ã�nAosuÈrlqdy{z|osq�js}3e?nAqfe?g�cfot}ã-G¾ � °)¡x|ã{v°b.o�cfy~osglom � r  q �< ÷ r� " ¸?jsh?g�okbdcie1bÂy~�)}3e?u~n3e?nlokb°glh5osb©glosjkosb.e?q.y~hokb.jsqdy{�ly~q�u{e?bxosjk}3e?jky{h)glokb�r3e?q.e�u{h)b]h?cfqdh)bxglhKnlh)b·tÅ��}lo�b.o�h)�ZcfosgAnlq��� e�osz|rlu{o°�e?glnlh)u{e?bokg�u{e?bposjk}3e?jsy~h)glokbÉ�)e|h?�Acfokgly{n3e1bÚv��

ü°ë ê�ë êKö°ë ²`h)b|�}lgAy{jsh?bÂglhKnlh)bÂy{g�cfokq.y~h)q.okbÂbdh)g�tL� � z�l � v�r�tm£4z�£�v`�¥tL� q z¡l q v�r�tÏ¡7z�£�v��e?u5jsh?glb.y~nlosq.e?q�uwe´y{g�cfokq.bdosjsjky��h)g�nAosu�nAh)zUy~gly{h´jsh?g���r £�o�l¹r £#b.o�jkh)gljsu~}A�)o��}lo�oku�glhKnlhÊ£�okbdc3�e#q.hKnlo�e?nAh#r^h?q�osu8glhZnAh'¡Ç�³u{h)b�glhZnAh)b�nlo�ÄÅqdh)g�cfokqfe tУ4z ç ¡{v��t�t�×Åx ç à4v�°)¡7z�£vÉ�atm£4zf¢�v���Æxo�ÄÅh?q.zUe��K}AoU¦3e�����}lo�jkq.o�e1q%}Ag3e�Ä1�h)q.z�}Auwe�nlo�jsy~gljshrl}Ag�c.h)b�okg�u{e´��}lo�nlh)b|nlo�u~h)b"«d�lqfe1Ãsh)bd¯"z|y{n3e?gÔ£Ç�\u{h)b�h?c.q.h)b?¸kr ç ¡hx�£��º�r�t ç à3x�£v¡°)¡K�ñ�¡

Page 101: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

££

¸º

»Âh?q5�Âe��Ku{h)q|~tLl±o»¸~v ¡ |~tLlv]oP| m t�lHv�¸¥oP| m m t�lHv�¸ q °)¡nz |�t�l(x+£v ¡ |~tLlv�x»| m tLlv�oP| m m t�lHv¡°?¡7 ��r�h)qpcie?g�c.h

| m m tLlv ¡ |�t�lVoa¸~vüoa¸~|~tLlÅx+£v�x¹tУDoP¸~v�|~t�lHvt�¸ q oa¸~v�°)¡  Æxo�u{e�z|y{bdz�e%ÄÅh)q.zUeu m m tL�]v ¡ º�uut��Åo £vüoduut��¥x)º�v�x¹tУZoaº1v:u�t��]vt�º q oaº1v¡°?¡  »Bh)qÉjsh)glbdy{�)}Ay{osg�c.o?�lbdo�h)�Zcfy{okglo�uwe�okjs}3e?jky��h)gÇe?bdhZjkywe?nle|e1u°glhKnlh�£º� q oË¢Vx�tУDoaº1v� �tLº q o»º�v�°)¡ o ¢eoP¸Û�M¡±x¹tУÂoa¸~v� �t�¸ q oP¸�v¡°)¡ r ¢7 ²©e\osjs}le?jsy��h)g okg osu*bdos�)}lgAnlh�glhKnlhËb.o´jsh)glbmcfqd}ly{qs�� eÊnlo³ÄÅh?q.zUe\bdy{z|y{u{e?qs�Ér�osq.hËuwebdy{z|okcfqs�� e�nlokuPrlqdh)�lu{okz�e*r�h)q8u{e%qdosj�cie.�âr¿×�°)¡Z�Ze?bdos�)}lq.e���}lo� � rå q u{h���}lo�u~u{ok±1eel � r  q r ç ¡Vx�£)�

ÌÎÍ ü°ëYê3ë êKü°ë tÏÓxz|y~cfy~nlh�vÑ�ÌÎÍ ü°ëYê3ë ê��©ë tÏÓxz|y~cfy~nlh�vÑ�ÌÎÍ ü°ëYê3ë ên�°ë tÏÓxz|y~cfy~nlh�vÑ�^#Ü _ @sà.B à�ç�áOâUä`WÊç\C�áOâUä�©ë ê�ë ê3ë �]u`y{g�cfok�)qfe?qpr�h)qpr3e1qdcfokbÉuwe�jsh?glnly{jky��h)g�nlo�¾*e?u{okq�ç�y{gx x/å m m o»å¥x+£4z $ �5y r ¢Hz

ñ4×

Page 102: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�Êbd}lb.yªcf}Ac.y{q0åÈr « �jë $ ë �8b.o�u{u~os��e#okgËc.hZnlh?b�u{h)b�j�e1b.h)b|ePt gÉ�h?c.osbdo���}lo $ � tY¢�v?r$ � tУv�r ¢�v B ë � � ëÞ� ër¿¼ � jsh)g � � ëIr t $ m � $ m ë o $ � $ ëèvÐz ¼ � r $ �a�gÇj�e?n3e�e?rle?qdcfe?nlh��3e?bmcie�}lbfe?qÉokbdcie�q.okuwe?jky��h)g�jkh)gÇuwe?bÈÄÅ}lgAjsy{h?glosbÉ��}lo*b.o%y{glnAy{j�e1g°�e�vȲ©e�y{g�±1e?q.y{e?gljsy{e�nlo*uwe�okjs}3e1jsy��h?g�r�h)qÈcfq.e?b.u{e?jsy~h)glokbpy{z|rlu{y~j�e

� �Ì� rÈ� qÌq r t¡t $ m � v q oÈt $ � v q v�r ��� ÷� ��� ÷ £�ë4�0oË¡ ��� ÷� � q ë��âr à?ÕîA£  Æxo�u{e�z|y{bdz�e%ÄÅh)q.zUe

� ��q r¿� q¡� r�x ��� ÷� ��� ÷ £�ë4�Åo $.$ � r�x ¡× o ��� ÷� t £× x��]vy��ë4�wr�x £�¢�ï£�Õ�¡  ¬Èe?u~js}lu{e?glnlhUosu��e?q.ose�nlosuBcfqdy��e?gl�?}lu{hUu{y{z|y~cfe?nlh�r�h)q $ �u¼ � r�¼ q r £�°{ñA��Æxo�z�e?gAosqfe��}lo*¦3e�����}lo*q.okb.h)uª±)osqÉoku`b.y{bmcfokz�e

ì à?Õ4°{îA£ x3à{×�°Z£�Õ�¡x3à{×�°Z£�Õ)¡ à?Õ�°{îA£�ð ì � �� q ð r ì £°{ñ£°{ñ*ð zh)�ZcfosgAy��osgAnlh)b.o|� � r5� q r�£�î�°4à{ñZ��IvGa�b��ly~osg�jkh)glhKjsy~nlhxnloku3e?gÉ�e?u~y{bdy{b©nloɧ3h)}lqdy{osqB��}loposgdÜ ¢Hz�£TÞZu{h?bGb.okglh)bv��jsh)bdosglh?btÅr^h)q�b.osrle?qfe?nAh�v�jsh)g�ÄÅqdosjs}Aosgljkywe?bpn3e1n3e?bpr�h)qÈz �}Au~cfy~rlu{h?b:okg�cfosqdh)bÉnlo � b.h?gÇh?qdcfh?�)h1�g3e1u{osbk�lnlo*z|hZnlh���}lo(� ë ë�r ¢�b.y�ØJÃrf$E�:»Âh)qÉh?c.qfe�r3e?qmcfo

�C����r �� t�D q � q jkh)b q t � D��]v�o�bdosg q t � D��]v�vZr D q � q oÔ£¡ z D1r�£4zi¡7zÚ×H �]nlosz��e?be¼ � r ¡{° � ��¼ q r ¢A��¼ ÷ r ¡4°t�× � v��O»Bh)qpcie?g�c.h� � r �� t � q o £v z � q r ¢Hz � ÷ r �× � t�ñ � q o £�v  

j�v]aOg�okbdc.o�j�e?bdh�glh�osb�r^h)bdy{�lu~o�e1rlq.h�±)okji¦3e?q�gly~gl�)}lgle�b.y~zUo�cfqs�� e|��u{h)b]j`�e?u~js}lu~h)bbdh)g�z��e?bpoѵZc.osglbdh)bs��h)�ZcfosgAy��osgAnlh)b.o� �Ì� r �� �Ðtm£�x\¡#�]v q o � q tm£�x)�]v q � ë4��r £)£×)¢� ��q r �� �Ðtm£�x\¡#�]v6tÏ¡#�¥x ×*� q vüo»�I÷#tУ�x)�]v q � ë��âr £)£

Õ)¢� qÌq r �� �ÐtÏ¡#�?x»×*� q v q o ��"*tm£òxA�]v q � ë4��r £ïñ?�

Page 103: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

»Bh)qÉh?cfq.e�rle?qdc.o}¼ � r�£°1ÕA��¼ q r £�°Z£¥¡Z��Æxo�z|hKnlh��K}Ao%bdo�u~u{ok��e�e?u`bdy{bdc.oszUeì £)£�°{×)¢ £)£°?Õ?¢£)£�°?Õ)¢ £°4ï»ð ì � �� q ð ríì £°?Õ£°Z£¥¡#ð

jk}A��e�b.h)u~}ljsy��h)g�osbs� � rÈà4°Z£)£?�!� q r ¢A��©ë ê�ë~ö°ë »�q.hKjsoknly{okglnlh|jsh)z|h|e?g�cfokbs�3¦3e�����}lo%j�e?u~js}lu{e?q� � ëIr t $ m � $ m ë o $ � $ ëÍvÄz ¼ � r � $ �

��nAosb.rA}��osb]q.osbdh)u~±?osq « � � ë�� ë�rȼ � �a�bdc3�e´jkuwe?qdh��K}Aod� �Ì� rg� qÌq r �q � ÷Ì÷ �>��}lod� ��q r � q ÷ r � q¡� r � ÷ q �:b.y~osglnlhoku�q.okbdc.hÊnlo#u{h?b¥� � ë5g�}lu{h)bk��Æxosu]e?r3e1qdcie1nlhÊe�v�nlosuxrAq.h)�lu~oszUe"e?g�c.osq.y~h)q|b.o�b.y~�)}lo� �Ì� rpà?Õ�°{ñ���� ��q r�x3à{×�°Z£�îZ�:¬�h)g�uwe�ÄÅ}lgljky��h)g $ e?u~uÒ�� y~g�cfq.hKnl}ljky{n3e¼ � r qy� ÷� � $ � ë4��r ��� ÷� ��� ÷ ×�tLå�o £× v $ ë4�âr ��� ÷� ��� ÷ $ r £ñ  

Æxo%uwe�zUy~b.zUe�ÄÅh)q.zUeA�I¼ q r&¡4°{ñA�É»Âe?qfe?¼ ÷ b.o�rA}losnlo�}lbfe1q���}lo $ ÷ tL�]vÂr ×#�âx�¡|okgbd}�bdh)r^h?qdcfo���bdo*nlosnl}Ajso.¼ ÷ r ��°?¡4ïZ�Oa�g�nAokÁ3glyªcfyª±?eZ�Aosu`bdy{bmcfoszUe�q.okb.}lu{e?g�cfo*osbÊÌ à?Õ�°*ñ x±à*×�°Z£�î ¢x±à{×4°Z£�î à?Õ4°{ñ x±à*×�°Z£�î¢ x±à*×�°Z£�î ¡{î4°{ñ

ÍÏ ÊÌ � �� q� ÷ÍÏ r ÊÌ £�°{ñ¡{°{ñ��°?¡4ï

ÍÏjk}A��e�b.h)u~}ljsy��h)gÇe?rlqdh�µZy~z�e?nle�osbt�� � zR� q z�� ÷ v�rÙt ¢ m £)£s��¢�¡s j j Äzi¢ m ¡?¢4×�¡)¡s j T Äzf¢ m ¡{×{ñ4ñ�às j j ¡vÄ 

�©ë ê�ë~ü°ë ��u`y~g�cfos�?qfe?qpr�h)qÉr3e?qmcfosb]e?¦lh?qfe�osu`cZ�okq.z|y{glh�nAo%ÄÅqdh)g�cfosq.ehå m � tm£v $ � tm£vÈglhbdo�e1gK}Auwe�r3e?q.e?ØhrÈ×Z�3nlo*zUhKnlh���}lo¼ ÷ r $ ÷ tУvüo �� � $ ÷ r�£Do �

¡4ï r ×A£¡4ï  

�]u`q.osbdh)u~±?osqÉosu`bdy{bmcfoszUe�e?g�cfokq.y{h?qÈjsh)gÇosbmcfo%j�e?z��ly{hl�Zuwe�b.h?u{}ljky��h)g�r3e1bfe|e�bdosqt�� � z�� q z�� ÷ v�rÙtУ°{×HzÑ¡{°{×Hz�£vРñ�à

Page 104: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

²©e5bdh)u{}Ajsy��h?g�e1rlq.h�µZy{zUe?n3e ¤åâr �÷ $ � o q÷ $ q o $ ÷ js}lz|rlu~o ¤å m tm£ � vNr q÷ t�x/×�vÐoU£7�è×.r£)�Éa�b]nlosjky{qs��bfeMcfy{bmÄ e?jso%osg<osbdc.o�jse?b.hUo�µAe?jkcfe?z|osg�cfo�u{e|jkh)glnly~jsy��h)g�nAo�ÄÅq.h?g�c.osq.eA�Éa�goku`rlq.h)�Au{oszUe�e?g�cfokq.y~h)qs�3e1u°¦3e?jkosqÉuwe�z|y{b.zUe�jkh)zUrAq.h)�3e1jsy��h?g�b.o*cfy{okglo¤å m tУ � v�r�tyx3×�v��¥¢ m ¡?¢4×)¡)¡s�����joa×±�¥¢ m ¡{×{ñ4ñ�às������r ¢ m £)£�¢A£� j j �©ë ê�ë¤�©ë ²©e�jsh)gAnly{jky��h)g�nlo�¾*e?u{okq�ç�y{g�u~u{ok±1e�e O \��rå\¼�jkh)g

� � ër �� � t $ m � $ m ë oÈtL��o�¡4v $ � $ ëÍv � ¼ � r¿¼ q r¿¼ ÷ r £¡  

¬�h)gÇj`�e1u{js}Au{h)bÈbdosgljky{u~u{h)bpbdo%rA}losnlo%ok±1e?u~}3e?qpu{e�r3e?qdc.o*nlo(� � ë �Ah)�Acfokgly��okglnlh)bdo �� � t $ m � $ m ë oË¡ $ � $ ëÍv�r 6 £���°*× b.y�Ø·r�$x%£)£°?Õ b.ys� Ø�xz$��4r&£

áÈe1bdcieUe� g3e?nly~qÉuwe�r3e?qdc.o�jkh)q.qdosbdr^h)gAnly{okg�c.o�ewý0� $ � $ ëÅ�5aObmcfh)b5±1e?u{h)qdosb5b.o�n3e?g#okg#uwey~glnly{jse?jsy��h)g°�Zo�µZjsokrAcfhwý·� $ qq ��}lo*osbÉcfqdy~±Kywe?u~zUokg�cfo�g�}lu~hl�OÆxo�osbmcie�ÄÅh)q.zUeO r ÊÌ £���°{× x�£?£°?Õ ¢x�£?£°?Õ £���°*× x�£)£�°?Õ¢ x�£?£°?Õ £���°{×

ÍÏ o ÊÌ x%£°?Õ x%£°1��î ¢x%£°1��î ¢ £°1�4î¢ £�°1��î £°?ÕÍÏ  

a�bÉnlosjky{qO r ÊÌ ñ�°)¡ x/î4ñ�°1�4î ¢x/î4ñ�°1��î £���°{× x�¡{ñ�°Z£�Õ¢ x�¡{ñ�°Z£�Õ ¡{ñ�°?Õ

ÍÏ�]u`q.osbdh)u~±?osqÉosu`bdy{bmcfoszUe�b.o*h)�Ac.y{okglot�� � zR� q z�� ÷ v�rÙt ¢ m ¡)¡{à{×?�� j j Äzi¢ m ¡4ï4ï)¡{×ò j T Äzf¢ m ¡?¢4ï1�l£� j j ¡vÄ 

�©ë ê�ëÍ�°ë ²`h)bÉosu~osz|osg�cfh?bpnlo*uwe�z�eMcfq.y~Ãxnlo*q.y~�)y{nAosÃ�±Ky{okglosgÇn3e?nAh)bÉr^h)q� � ër t $ m � $ m ë o $ � $ ëÍvÄ 

¬�h)z|h�uwe��}luªcfy{zUe%ÄÅ}Agljsy��h)g��3e?b.o*okbdc��e�jsh?qdcie1n3e|r�h)qpu{e�zUyªcie?n°�� �Ì� rÈ� qÌq r ������r £

¡ ��½�½� ñ)Õ

Page 105: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�]nlosz��e?b � ��q r¿� q¡� rÈ� q ÷ rÈ� ÷ q r ������r¿��½ � � ½»r¿��½1½ � �  a�uAqdosbmcfh*nloÈu~h)bvosu~osz|osg�cfh?bvb.h)g�g�}lu~h)bs�Ga�bdcie1b:jse?g�cfy~n3e?nlokbvb.h)g�bdosgljky{u{u{e?bGnAoÈj�e?u~js}lu{e?qnly~q.okjkcie1zUokg�c.o�hUjkh)gÇ}lg�j�e?z��Ay{h�nlo�±1e?q.y{e?�lu{o1��a�u`q.okb.}luªcie?nlh�okb� �Ì� r qy� ½� û q ë4�·o�¡ ��� ½� û q � q ë4��r ¡*ûäo ¡×4û� ��q r qy� ½��� ½ x/û²��ûgë4��o�¡ ��� ½� û��1tm£ex»û¶�]vNë4��r�x/û=o £

Õ4û  �©ë ê�ëÍ�°ë ºZoxrl}loknlo*e?bdhZjkywe?q�e�j�e?n3e�ÄÅ}Agljsy��h)g��3e?bdo�osu^glhZnAh���}lo�osbmc��e�osg�okuPrl}lg�c.hz|osnly~h]nAo8bd}�b.h)r�h)qmcfo?tü� ¬ r&£�o|N7°M�l¸?N0r&£4zÑ¡7z�×A�B»Ge?q.e���}lo�¦3e��)e]��}ly{gAjso8ÄÅ}Agljsy~h)glosb�3e1b.o:b.o�nAos��osqs�� e?g�jkh)glbdy{nlokqfe?qBu{h)b©glhKnlh)b�� ¬ r�£4orNn°Z£�ÕA¸3NÅr £4zÑ¡nzj j j Äz�£àZ�Âa�bGnlokjsy~qs�

u{e�ÄÅ}Agljsy��h)gU�le?b.o ¤$ ¬ nAos��o]bdosq $ e�·d}lbdcfe?n3e�e1u3y{g�cfokqd±1e?u{h?Ü � ¬ � � z�� ¬ � � ÞY��²©e%¦Ah)zUh1cfosjkywejkh)z��ly~g3e?n3epjsh?g�}lgle5cfq.e?b.u{e?jsy��h)g���}lo:r3e?bfeÅÜ � ¬ � � z¡� ¬ � � Þ r�Üèt N�o|£à4v¡°K£�ÕHzt�N�oU£ï4v�°Z£�Õ*Þe¶ÜΣ4zÚ×�°)¡Þ`osbò�{G ¾ �{�¥x�tm£)£DoÝN7v�°1�l�lu~h�js}3e1u`rlq.}lok�3e  $ ¬ tL�]v�r $ t �{�?x �Ì� � ¬" vÑ�²©e�jsh)glnAy{jsy��h)g�nlo�¾%e1u{osqRç�y{g�osgÇosbmcfo%j�e?bdhUy~zUrAu{y{jse¤ � � ër ��¤$ m � ¤$ m ë  ºZ}Abdcfyªcf}A�?osglnAhU��jse?z��ly{e?glnlh�u{e�±?e1q.ywe1�lu{o¤ � � ëIr � $ m � �{�¥x £)£DoãØ

� � � $ m � �{�?x £)£Do�$� � ë4�r �Ìå�o £)£ZoPØ

� � $ m t�å]v $ m ��å¥x Ø·xz$� � ë�å� 

²`h)b#�}lgly~jsh)bpoku{okzUokg�c.h)bÉglh�g�}lu{h)bÉjk}3e?glnlh|$ æ¹Ø�b.h?g¤ � ��� r å1t $ m � v q ë�å�o £)£DoãØ� t $ m � v q ë�å¤ � ��� � � r å $ m � $ m q ë�åÅo £?£ÂoPØ� $ m � $ m q ë�å

nlh?glnlo $ � t��]v�r $ t��]v8� $ q t��]v�r $ t��¥x�£°M��v��²©e�z�e1c.q.y~Ãxnlo*q.y~�)y{nlokÃ�nlosu`okg�}lgljsy{e?nlh|y{z|rlu{y~j�e å1t $ m � v q ë�åâr ¡*×4ñ

�4î � å $ m � $ m q ë�åwr�x £ï£¥¡  ñ�ï

Page 106: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

»Âe?qfe�¦3e?u~uwe?q�uwe?bpy~g�c.os�)q.e?u{okbpq.okbdcie1g�c.osb5b.o*rl}loknlo%osz|rlu{ose?qÈ}lgÇj�e?z��ly{h�nlo�±1e?q.y{e?�lu~oñ�ï£�Õ r å1t $ m � v q ë�å¥r tL��o £

� v6t $ m � v q ë4��r ¡*×4ñ�4î o £

� t $ m � v qx à× r å $ m q $ m ÷ ë�åâr tL�·o £� v $ m � $ m q ë4�âr�x £ï£¥¡ o £

� $ m � $ m q  Æxokb.r�oз.e?glnAhl��ý�t $ m � v�qÛr £j×�°Z£¥¡#�Pý $ m � $ m q r x%£)�}�Úb.}lbmcfyªcf}A�?osglnlhA�pb.o<h?�Acfy~osgloÁ3gle?u{z|osg�cfo ¤ � ��� r ¡{×4ñ��î o £?£Zo�Ø

� � £�×£¥¡ r ×4î�¡�oÔ£�×�Ø��î¤ � ��� � � r ¤ � � � � � r�x £ï£¥¡ o £?£ÂoPØ

� �nt�x%£vNr�x à?¢eoP×�Ø£¥¡  a�u`q.okbdc.hUnlo*u~h)bposu~osz|g�c.h)bpnlo*uwe�zUe1c.q.y{Ã�nlo*q.y{�?y{nlokÃ�b.h)gÇg�}lu{h)bk�

�©ë ê�ë � ë ��uBe?rlu~y{jse?qposuBz\�o�cfhKnlh|nlo�nAy~ÄÅosqdosgljkywe?bÉÁ3glyªcie?b5osu©bdy{bdc.oszUeU��}lo�¦3e�����}loqdosb.h?u~±)okqÉosb x  � � � oé �#� � x�¡¢Â �£�°Tû q rp| �jkh)g�¢�r £4zÑ¡7zT j j ÄzÚûêx £���nlokÁlgly{okglnlh Â1�±r Â�½ � � r�¢A�x²BeUz�e1c.q.y~Ã�jkh)q.qdosb.r�h)gZ�nly~osgAc.o�osbÉcfqdy{nly{e?�)h)g3e1u^bdy{z\�okcfqdy{jseA�Ajkh)gÛ�C����r ¡{ûdq5���C����� � r�x/ûdq¥�»Âh?q�h?cfq.e>r3e?qmcfo�e?u�e?rlu~y{j�e1qUoku�z\�okcfhKnlh>nAo�osu{okzUokg�cfh)b�Álgly~c.h)bs�Éosg�okbdc.o�j�e?bdh� � ërpý $ m � $ m ë nlo*z|hZnlh���}lo*uwe�zUe1cfqdy{Ã�±K}loku~±?o�e�b.okqpcfq.y~nlywe1�)h)g3e?u�b.y~z\�o�cfqdy{j�e�jkh)g

� �`�ur qy� ½� û q ë��âr ¡{û¶z �C����� � r qy� ½��� ½ x/û q ë4�âr�x3û¶z��}lo*jsh?y{gljky{nlo�jkh)g�u~h|e?g�cfosqdy{h)q�bfe?uª±)h|}lgÇÄ e1jkcfh?q�û³�

�©ë ê�ëÍ °ë ¬�h)g�u{e%gAh?cie?jky��h)g|nloku^rlqdh)�lu~oszUe%e1g�c.osqdy{h)qÂ| � rÈ���|oku�±?osj�cfh)q8nlo�jse?q.��ec.y{osgAo�nlo�jshKh)q.nlokg3e?n3e1b}¼��Drkýh� $ ��rk�V°Tû³��»Âh)q�cie1g�c.h�u{h)b�bdy{bdc.oszUe?b�h)�Ac.osgly~nlh)be?u�e1rlu{y~j�e?q�u~h)bOz\�o�cfhKnlh)b:nlo]nAy~ÄÅosqdosgljkywe?b�Á3gAy~cie1b:��nlo5osu~osz|osg�cfh?b:Á3gAy~cfh?b8bdh)g�y~�)}3e?u~osbtÅbfe?uª±)h*b.y~zUrlu~y~Á3jse?qB}lg|Ä e1jkcfh?qNû�vG��bdoÉc.y{okglom� � r  � �G»Âh)qOh?c.qfexr3e1qdcfo1��uwexb.h?u{}ljky��h)goѵle1jkcie�osb}å1tL�]v3r x/�V�1tm£VxP�]v�°)¡Z�©}lg'r�h)u{y~glh)z|y{h�nAo|bdos�)}AglnlhÇ�)qfe?nAhl�`nlo�zUhKnlh��}lo*uwe�Ä1�h)qdz�}lu{e�b.y~�)}ly{okg�cfo*osbÉo�µAe?j�cieå m m tL� � vNr å�t�� � � � vüo»å1tL� �*� � v�x�¡*å1tL� � v£�°Tû q z

ñ4î

Page 107: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�?��osgÊjsh?glb.okjs}lokgljsy{eA�:e?uÈe?rAu{y{jse?q%osu�zÊ�okc.hZnAh#nlo�nlyªÄÅosqdosgljkywe?b%Á3gly~cfe?bJ � r²å1tL� � v��av±Ky{nlokg�cfosz|osg�c.o?� B � ë $ ë�tL� � vNr B  ë $ ë�t�� � vNrå � ��£/rÈå1t�� � vР�©ë ê�ëÍ&°ë a�b.jkq.y{�Ay{osgAnlh $ ÷ tL�]v�r $ � tL��x|£v��?u{h)bBosu~osz|osg�cfh)bBnlo8uweÉz�e1c.q.y~Ã:nAo�q.y~�)y{nAosÃ��oku°±)okjkcfh?q5nAo%jse?q.�)e�±Ky{okglosgÇn3e?nAh)bÉr^h)q

� � ë�r t $ m � $ m ë o $ � $ ëèv � ¼ � r t�� q x�¡#�?x�¡4v $ �  avÄÅosj�cf}3e1glnlh|u{h)bpj°�e?u{jk}lu{h)b

� �Ì� r �� t¡t �}x î#�]v q o $ q � v�ë4�âr £�Õ× o î£�à r î4î

£à� ��q r �� t¡t �}x î#�]vTt �*�wx+£vüo $ � $ q v~ë4��r�x î× o ££à r�x £�×à� qÌq r*¡ �� t¡tÅ�{�¥x�£�v q o $ qq vNë��wr £��× o �

£à r ï1�£à  

�]nlosz��e?b/� q ÷ rÝ� ��q rÝ� q¡� rÝ� ÷ q �d� � ÷ rÝ� ÷ � r�¢A�ɲ©e?b5jsh)z|r�h)glosg�c.osb�nAosu©±)osj�cfh)qnlo*jse?q.��e�bdh)g¼ � r �� �*�1tm£�x)�]vTt�� q x\¡�wx\¡4vNë4��r x ñ༠q r ¡ �� �1tY¡#�wx�£�vTtL� q x�¡#�?x�¡4v~ë4��r�x ×A£×)¢ z ¼ ÷ r¹¼ �  

Æxh)gAnlo�b.o%¦3e�}lbfe1nlhUu{e�b.y~zUo�cfqs�� e�r^h?qs��r £*nloV�IqZx�¡#�¥x�¡K���u©qdosb.h?u~±)okqÉosu©b.y~bdcfokz�e O \�dr \¼xb.o%h)�Acfy~osglo|� � rc� ÷ rÙx3×4°1�l�#� q rÙx%£)�8»Ge?q.e�Û¦»Ü ¢7z�£TÞ B � ë $ ë�tL�]v�r�x ×� �{�1tm£�xA�]v�xA�1tY¡#�wx+£�vZré� q x�¡�� »Bh)q]u{eUbdy{z|okcfqs�� eA�AosbdcfeUÄ1�h)qdz�}luwe�cfy~osglo*±1e?u{y~nlosÃ*okg<cfhKnlhÛÜ ¢Hzi¡#ÞÏ�ɲ©e�ÄÅ}lgljsy��h)gÛå1t��]vsr�IqZx\¡#�<osbÉok±Ky{nAosg�cfokzUokg�c.o�u{e�b.h)u~}ljsy��h)g�o�µAe?jkcfeA�

ÌÎÍ �©ëYê3ë ê�+`ë tÏÓxz|y~cfy~nlh�vÑ�ñ4ñ

Page 108: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ÌÎÍ �©ëYê3ë ê�ê3ë tÏÓxz|y~cfy~nlh�vÑ��©ë~ö`ë ê3ë aObmcie�okjs}3e?jky��h)g�gAh�osbpz��e?b���}lo�u{e�ÄÅh)q.z�}luwe?jky��h)g|n8�ok�ly{u^nlosu°rAq.h)�lu~oszUe�nlojkh)g�cfh)qdglh xeå m m o\�4åhx�£3r ¢Hz å1tY¢4vNrÈå1tm£°)¡{v~r ¢H 

»Âe?qfe�qdosb.h?u~±)okq.u~hl�`gÉ�h?c.osb.o���}lo�xeå�m m�o+�4åJr ¢{� å\r O újq � o5^Åú � q � �°�#��}lo�}lglebdh)u{}ljky��h)g�r3e?qmcfy~js}lu{e?q�nlo<u{e´gAh"¦lh)z|h)�Â�okglo�e'osb?åÝr £°1�l�ÔÆxoÇzUhKnlh'��}lo<�le?bdcfee¥·d}Abdcie1q O �]^ okg å1tL�]v�r £� o O ú q � o°^�ú*� q �r3e1qfe'�K}Ao�bdo�jk}lzUrAuwe?g\uwe1b|jkh)glnly~jsy~h)glosb�nloÇjsh?g�c.h)q.gAhl�+a�uÉq.okb.}luªcie?nlh'okb<£° O rx5�Itm£Doaúv��`£°,^�r�x5�ItУÂoaú � ��v��

�©ë~ö`ë~ö°ë ®Eg�cfok�)qfe1glnlh|r^h)qprle?qdc.osbs��u{e�ÄÅh)q.z�}Auwe?jky��h)g�n8�os�ly~u°osb� tLå�z�òHvNrȪ/t�ò7v jsh?g � t�å�z�ò7vNr t��Iå m ò m o�¡*å�ò7vÄz ª/t�ò7vZr5ò

nlh?glnlo±å�z�ò?¦¥ô\�Obdo�«.e?g�}lu{e?gl¯�okg�£)��»Ge1qfe�okÄÅokjkc.}3e?qÈu{e�y{g�c.os�)q.e?jsy��h)g�r�h)q�r3e1qdcfokbÈosbj°�h)zUhKnlh*glh?cfe?q���}lo(xe�Iå�m m6xâå�m7r�x�t��Iå�m¤vymw��»Ge?q.e�e1rlu{y~j�e?qvoku3z\�o�cfhKnlh*nlo5osu{okzUokg�cfh)bÁ3gAy~cfh?bp¦3e�����}lo�jse?u{jk}luwe1q� t $ � z $ � v�r ÷� �w�)£ q ë4�·o\� q� tL�¥x+£v q ë4��r £�Õ×� t $ � z $ q v�r ÷q �w��tyx�£v~��£eë4�0oË¡ ÷q t�×Vx)�]v6tL�wx�¡{v~ë��âr�x £�×Õ� t $ q z $ q v�r ÷q tL�¥��£��)£Do�¡tY¡VxA�]v q vNë4��r £jñ

Õ  »Bh)qÉh?cfq.e�rle?qdc.o}ª/t $ � vNr £?��ªet $ q vNr�£°)¡Z���]b��� rl}lokb]¦le����K}Ao�qdosb.h?u~±)okq

ì £�Õ4°{× x%£�×�°?Õx%£�×�°?Õ £�ñ4°?Õdð ì � �� q ð r ì ££°?¡{ðjk}A��e�b.h)u~}ljsy��h)g�osbs� � r&£à{×�°M��×4ñA�!� q r £ïM��°1��×4ñZ�

£�¢)¢

Page 109: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�©ë~ö`ë~ü°ë »Bh)qÉuwe�q.ok�)uwe�nloku`rlq.hKnl}lj�cfhnly~±ut}ò O tL�]v�Ô·å]vZr ÷B � 2 � ì Æ�òÆ��� t O t��]v�Ôhå]vn�7o°ò ÆÆ��� t O t��]v�Ô·å�vn� ð  

Æxh)gAnlo�osu`bd}l�`�� gAnly{nlo³DOy{gAnly{jse�uwe�jshKh)qdnlosg3e1n3eD�x��okb.y~z�eA�ÆxoxÄÅh)qdz�e���}lonlyª±üt�ò O tL�]vRÔhå]vNr�tiÔ�ò7v ­ O tL�]v�Ô·å0ovò�nly~±ut O tL�]vRÔhå]vÄ 

»Bh)qÉosbdcfe|y~�)}3e?u~n3e?n���osu°cfokh)q.okz�e�nlo*u{e�nAy~±)okq.�)okgljsy{ex ä ò�nlyª±�t O tL�]vRÔhå]vNr ä tLÔò7v ­ O tL�]vRÔhå·o Ç�ä ò O t��]v�Ôhå� 

»Âe?qfe|y{z|r^h)gAosqpuwe1b5jkh)glnly~jsy~h)glosbÉnlo%jsh?g�c.h)q.gAh�b.o�rlq.hKjsoknlo%y{�)}3e1u`�K}Ao�jkh)g<okuBu{e?rlu{eM�jkywe?glhA�»Bh)qBoзdosz|rlu~hl�1�le¥·dh]jkh)glnly~jsy~h)glosb©¦lh?zUh)�Â�osglose?bÂnAo�Æxy~q.y{ji¦Au{okc°h]nlo8­]ok}lzUe?glg°�okbdcfh|osbk��å ùù Ç�ä r ¢|h Ç�ÒÇ�Ó ùù Ç�ä r ¢A¸�tÅc.qfe?�le¥·.e?glnlh|osg�ô\�� t}Å�v�hlôJ�6tLÅ�v�v�b.o*cfy{okglo�]tLå�z�ò7vNr !ä tiÔ�òHv ­ O t��]v�Ô·å � ªet}ò7v�r #ä |OòI 

²©e?b]jsh)glnAy{jsy~h)glokb]nlo�­]ok}lz�e1glg#glh�¦Ah)zUh?�G�osglose?b]e� g3e?nly~q��� e1gÇ}Ag<cZ�okq.z|y{glh|nlo�ÄÅqdh)gZ�c.osqfe�ehªet}ò7v��ljkh)z|h|okg�oku`j�e?bdhUnAosu`uwe1rluwe?jkywe?gAhl��©ë~ö`ë¤�©ë ¬Èe?z��lywe?gAnlh#nlo�bdy{�)glh<o�y{g�cfok�)qfe?gAnlh#r�h)q�r3e?qmcfokbs�Ob.o�c.y{osgAoâ� t�å�z�ò7v0rý·åIm`ò�mw��ªet}ò7v�r�x�¡�ýò��l��u{e�ÄÅh)q.z�}Auwe?jky��h)g�±1e?qdywe?jky{h)gle?u°e1Álq.zUe��K}Ao�u{e�o�µZrlq.okb.y��h)g

£¡ � tLå�z¡å�v�x ªet�å]v�r £

¡ t�å m v q o�¡ åe?u~j�e?gAÃ�e�}lgÇz<�� gly{z|h�r3e1qfe0åâr¹�Iq�o £?�OaObÉnlokjsy~qs�

£¡ �� � � t�å m v q o��4å � æ £

¡ �� � � tÏ¡�]v q o��It�� q x+£�v � ë4�� �]u`h)r^okqfe?qpbdo*h)�Acfy~osglo*u{e�nlosbdy{�)}3e1u{n3e?n�nlokb.ose?n3eA�

£�¢A£

Page 110: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

� �©ë~ö°ë�� ºZyZåÊosb�}lg3e�ÄÅ}lgljsy��h)g"jkh)z|h�okg>osu:osg�}lgljkywe?nAhl�Gbdo�e�öär;å¶x�� q o&£)�okg�c.h)gljkosb �� � � tLå m v q o��{å � r �� � � t}ö m v q o\�{��ö m o\�Cöaoãà� q xÊ� � ë4�r î× o �� � �Út}ö m v q o��It���öVv m �æ î× o �� � tL��ö±v m r î× o\�Cö0tУvuo��,ö0t�x%£vNr î×  

�©ë~ö`ëÍ�°ë Æxokq.y~±1e?gAnlh x�td ��t��]v�å m v m r�x� � tL�]vyå m m x  � m tL�]vyå m znlo*ÄÅh)qdz�e���}lo��le?bdcfeUrlqdh)�3e?q5��}lo�oѵAy~bdc.o� ��cfe?u©�K}Aoât�x� �Izjx� �4m vp��tyx3��zÚ¼Äv5bdh)g<rAq.h1�r�h)q.jky{h)gle?u{okbs�Aokbdc.hUokbs�

¢.r ùùùù x� � x3�x� �4m ¼ ùùùù r� � m �Åx� �n¼� ²`h�jk}3e?uZu{u{o�±1e]e�okb.jkh)�)osqp �0rÈú ��~ þ � ÿ �?�%uwe5ÄÅ}Agljsy��h)g�r�h)qGu{e]��}loȦle��%��}loÈz�}lu~c.y{rlu~y{j�e1qokb� �n°{�3�®Eg�cfok�)qfe?gAnlhUr�h)qpr3e1qdcfokb]bdo*u{u{ok��e�e�uwe�ÄÅh)qdz�}lu{e?jsy��h)g�n8�ok�ly{u�� t�å�z�ò7v~rȪ/t�ò7vpjkh)g

� t�å�z�ò7vNr tm ��å m ò m o  @ÐåVò7v � ªet�òHv�r  |�ò  �©ë~ö`ë � ë ºZy~�)}ly~osglnlh�u{e�y{glnly~j�e?jky��h)gÄ t Ä å]v�r Ä ì Æ q åÆ� q o Æ q åÆ�l q ð r Æ " åÆ�� " o�¡ Æ " åÆ� q Æ�l q o Æ " åÆ�l "  

Æxo%z�e1glosq.eU��}lo�u{e|okjs}3e?jky��h)g<nlosuBrlq.h?�lu{okz�e�osb Ä t Ä å]vsr�|Â�]��}luªcfy~rlu{y~j�e?glnAh|r�h)qò|��e?rlu~y{j�e1glnlh�uwe�y~nlosg�c.y{n3e?n�nlo�¾�q.okosgÇb.o%nlosnl}Ajso ä ò Ä t Ä å]vZr�x ä Ô·å?�1Ôdt Ä å]vüo Ç�ä ò!Ôdt Ä å]vNr�x ä ÔÛt Ä å]v��1Ô�ò  

�]rlu{y~j�e?glnAh�nlo�g�}lok±?h�uwe�y{nlokg�c.y{n3e1nÇnAo%¾*qdososgÇe�uwe��}luªcfy~z�e*o�µZrlqdosb.y��h)g°�3r�osqdhUe1¦lh)qfer3e1qfe�nlosbdr^oE·.e?q/ýlÔÙ�1Ô��3b.o�cfy~osglo !ä ò Ä t Ä å]vNr !ä Ä å Ä ò.x #Ç�ä Ä åOÔò�r #ä Ä å Ä òI 

£�¢�¡

Page 111: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

a�u°cZ�okq.z|y{glh�nAo*ÄÅqdh)g�cfokqfe�b.o�e?g�}luwe�r�h)q.��}lo�Ô�òÅ� í r�Æ�ò7°,Æ í r ¢A��©ë~ö`ëÍ °ë ²©e�nlosqdy~±1e?n3e�n8�ok�ly{u`nAoÅ| � osb

| m� t��]vZr 6 ¢ b.yu�Û¦»Ü x �q � z �q � Þ¢ b.yu�Û¦»Ü x�£4zs£TÞ�x¹Ü x �q � z �q � Þ»Âe?qfe�jkh)z|rlq.h)�le?q.u~h�q.y~�)}lqdh)bfe?z|osg�c.o"jsh?g uwe�nAokÁ3gly~jsy��h)g°�*�3e?bmcie+glh?cfe?q<��}lo"r3e?qfejk}3e?u{��}ly~osqÈÄÅ}lgAjsy��h?g $ ¦��0�� �lbdo%c.y{okglo

| � $ m r � ����q �� � £¡ $ m o �����q � £¡ $ m oa¢ ����q �� ����q � � $ m r x/¢ ����q �� ����q � $ z

nlh?glnlo#bdo#¦3e>y{g�c.os�)q.e?nlh>r�h)q�rle?qdc.osb�oku"�}lu~c.y{z|h'b.}lzUe?glnlhA�&¬�h)g�osu~u{hAý¥| � $ mVrxJý?| m� $ �¶| m� okbÉq.o�e1u{z|osg�cfo�u{e�nAosq.yª±1e?n3e�n8�os�Ay{uÏ�a�bÉok±Ky{nlokg�cfo%�K}Ao�X6| m� X � r�£)��e1b��� ��}loÅ| m� okbdc��e�}lglyªÄÅh)q.z|osz|osg�c.oxosgdª � �»Âh?q5oku°cfokh)q.okz�e�nloku°±?e1u{h)qÈz|osnAy{h�r3e?q.e|y~g�cfos�?qfe?u~osb

����q �� ����q � u0r £¢ uut�� � v jkh)g � � ¦»Ü¤x £¡*¢ z £¡*¢ Þ� 

»Bh)qpcie?g�cfhu~y{z� ­ 0 �� � | m� u·r u~y{z� ­ 0 ¢

����q �� ����q � u0r u~y{z� ­ 0 ¢��£¢ u�t�� � v�r5u�t ¢�vÄ 

ºZy5o�µZy~bdcfy~osq.e�I ¦kªÂ�|��}lo<ÄÅ}lokqfe"uÏ�� z|y~cfo�nlo�| m� �Èbdo<cfokglnlqs�� e ý I³u¹r uut ¢�v�r3e?qfejk}3e?u{��}ly~osqmu¥¦��¥t�ܤx%£4z�£6Þ�vÑ�OaOgÇr3e?qmcfy~js}lu{e?q�ýJIpr £���r^h?qpoзdosz|rlu~h

I?tL�]vòtУex»ú*��� � � vNë4��r ¢H »Bosq.hÇcfh)zUe?glnAh�uÏ�� z|y~cfokbs�°okbdc.h<jsh?g�c.qfe?nAy{jso|osu�c.osh)qdoszUeÇnlo|uwe�jsh?g�±?osqd�)osgljkywe<nAh)zUy �g3e1n3e�r^h)qd��}lo�£ex»ú ��� � � ¾ £%osgÇj�e?bdy°cfhKnlh�rl}lg�cfhA�ÌÎÍ �©ë{ö°ëÍ&°ë tÏÓxz|y~c.y{nlh�vÑ�ÌÎÍ �©ë{ö°ë ê�+`ë tÏÓxz|y~cfy~nlh�vÑ�

£�¢4×

Page 112: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�©ë~ü`ë ê3ë ²©e|ÄÅ}lgljky��h)g $ � o $ q o $ ÷ t7§ q x�¾ §�okb�u{y~glo�e1u`osg¥ø ��okg#j�e1n3eU}lgAhnlo*bd}lb5c.q.okbɱ��okqdcfy~jsokbɱ1e?u~o�£)�lr�h)qpcie?g�c.h|nAos��o%bdosq5jsh)gAbdcie1g�c.osz|osg�cfo|£)��©ë~ü`ë~ö°ë ºZose|u{e�g�}lzUokqfe?jky��h)g�nlo*u~h)bpglhKnlh)bÉjsh)z|h�b.y~�)}lo1t

£3¾ t�x%£4zi¢4vÄz ¡}¾ t ¢Hzjx%£vÄz מ tm£{zi¢�vÄz �.¾ t ¢Hz�£vР²©e�ÄÅh)q.z�}luwe?jky��h)g�n��os�ly~u`u{u~ok±1e�e� t�å�z�ò7v~r ä tLÔhå?�1ÔòVo»å�òHv � ª/t�ò7vNr ä òI ¬�h)z|h¥å�bdo�e?g�}lu{eUokg#u{h)bÉglhKnlh)b3×|�Ç��u{eUbdh)u{}ljky��h)gÇr�h)q]okuÂzÊ�okc.hZnAh�nlo�osu{okzUokg�cfh)bÁ3gAy~cfh?bUbdosq3�e´nlo<u{e'ÄÅh?q.zUeJåpr�� � $ � o�� q $ q �\cfhKnlh´u{h´��}lo<¦3e�����}lo<¦le?jsokq�osbqdosb.h?u~±)okqÉosu`b.y~bdc.oszUe ì � t $ � z $ � vX�]t $ � z $ q v� t $ q z $ � vX�]t $ q z $ q v ð ì � �� q ð r ì ªet $ � vªet $ q v ð  »Âe?qfe#¦3e1jsosq�u{h)b�j`�e?u~js}lu~h)bs��bdo�e¥ø osu:cfq.y��e?gl�)}Au{h"£��m¡¥�Ò�l�'¬�h)z|h $ � txø x]¾ §Øosb}lgle³ÄÅ}lgljky��h)g+u~y{glose?uÉ��}lo<±1e?u{o³£#osg�oku]gAhZnlh�£<�+¢³osg�u{h?bUh?c.q.h)b�nlh)bs�Ébdo<cfy~osglo$ � tL��z�lHvNr�x��Çosgaø>�OÆxo5uwe%zUy~b.zUe*ÄÅh)qdz�e $ " t���z�lHvNr�tm£�o���x�lHv¡°)¡*osg]ø>�:¬�h?goku{u{hA�

� t $ � z $ � v�r ! tУDo»� q v~ë4�âë�l·r&£Âo �� � � � �� � � � � q ë4�âë�l0rïÕ� t $ � z $ q v�r¹x £

¡ x �� � � � �� � � ��¡ tm£Do»�¥x lv�ë4�wë�l0r�x à

£¥¡� t $ q z $ q v�r�£Do �� � � � �� � � �£¡ tУZo»�¥x lv q ë4�wë�l�r � ×  

»Bh)q*h?cfq.eÇr3e1qdcfo1�Âjkh)g´uwe�Ä1�h)q.z�}luwe�r3e?q.eÇokuv±)h)u~}lz|osg´nlosu�cfo�cfq.e?osnlqdhÛªet $ � vVr�£�°{×A�ªet $ q ver�¡4°{×A����uGbd}lbdc.y~c.}ly{qxokg�osuÂb.y{bmcfokz�e���q.okb.h)uª±)osqdu{hl�^b.o�c.y{osgAo<� � r £�¢?��°Z£�ñ{ñA�� q r £�×�¡{°Z£�ñ4ñA�Ó�cfq.e�ÄÅh?q.zUe�nlo*¦3e?jkosqposuPrlq.h)�Au{oszUe�osbÉ}Ac.y{u~y{Ã�e1glnlh�u{e?bpzUe1cfqdy{jsokbÈ�É�e?bdy{jse?bs���Bqfe?b}lgAh)b�j`�e?u~js}lu~h)b]c.osnly~h)b.h?bs�`b.o�rA}losnlo�h?�Acfokglosq���}lo�uwe1b�zUe1cfqdy{jsokbx��}lo�jsh?q.q.okb.r�h)glnlokge?u©cfqdy��e?gA�)}lu{h|nlo�u{eUnlokq.okji¦3e��<nlo�uweUy~Ãs��}ly~osq.nleA�^g�}lz|osq.e?nlh)b�jsh)z|h�¡¥�Ì×M�E���"£��m¡¥�Ò�l�bdh)g�qdosbdr^okjkcfyª±1e?zUokg�cfo

££�¡ ÊÌ î x3à £x3à £s� x3࣠x3à î

ÍÏ � ££¥¡ ÊÌ £�� x±à x3àx±à î £x±à £ î

ÍÏ  £�¢?�

Page 113: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�]u�okglbfe1z��luwe1q:u{e%zUe1c.q.y{ÃpnAo]qdy{�)y~nlosÃ1�Ku{e?bOnlh)bÇ�}lu~c.y{zUe?bGÁ3u{e?b��Ujkh)u{}AzUg3e1b:bdo]rA}losnlokgnlokb.rlqdosjkywe?q:r^h?q:u{e�jsh)glnAy{jsy��h)g|nlo�Æxy~q.y~ji¦lu{o�c��?��u{e?bOh?cfq.e?b8nAh)b8nle?gUu~}l��e?q:e*uwe�zUe1cfqdy{á0£�¡�nlosu`bdy{bmcfoszUe�e?g�cfokq.y{h?q.z|osg�cfo�qdosb.}Aosu~c.hl��©ë~ü`ë~ü°ë ¬�h)gAb.y{n8�osq.okb.o%uwe�g�}lz|osqfe1jsy��h?gÇnAo%u~h)bÈglhKnlh)b£3¾ tУ4z�£vÐz ¡(¾ tY¡7zÑ¡4vÐz ×(¾ tY¢HzÑ¡{vÄz �ž tY¢Hzi¢4vÄz à(¾ tÏ¡7zi¢4vÄ 

²©e�jsh?glnly{jky��h)gâå1t ¢Hz�lHv�rÈå1tL��zf¢�vNr ¢�y{z|rlu~y{j�e*��}lo*b3�h)u~h�uwe?b8ÄÅ}lgljsy~h)glokbÉe?b.hKjsy{e?n3e?bpeu~h)bpnlh)bÉrlqdy{z|osq.h?bÈglhKnlh)bÉr3e?qmcfy{jky{r3e1g�osgÇuwe�b.h?u{}ljky��h)g°�Oa�bÉnlokjsy{qk��åâr�� � $ � ov� q $ q �²©e�ÄÅh)q.z�}Auwe?jky��h)g�n8�os�ly~u°cfy{okglo�jsh?zUh�ÄÅh)qdz�e��ly~u{y~glo�e?u���u{y~glo�e1u°e� t�å�z�ò7vNr !ä Ôhåh�1Ôò � ªet}ò7vNr q� ò]tL��zÑ¡4v~ë4�� 

ºZoseløøoku`cfq.y��e?gl�)}Au{h�£k��à��m¡Z��aOg �osu $ � tL��z�lHvÂr�¡Vx �#� $ q t���z�lHvDrktL�·oPl�x�¡4v�°)¡Z�¬�h)gÇosu~u{h� t $ � z $ � vNrx� ! XpÔ $ � X q r �� t $ � z $ q vNr*¡ ! t�x%£4zi¢�v��nt £¡ z £¡ vNr�x�£� t $ q z $ q vNr*¡ ! XpÔ $ q X q r�£

Óx��±Kywe?z|osg�cfo}ªet $ � v�r ¢��wª/t $ q vNrpý q� �]°)¡}ë4��r�£?�O»Âh)qpcie1g�c.h�¦3e�����}lo*q.okb.h)uª±)osqoku`b.y{bmcfokz�e ì � x�£x%£ £wð ì � �� q ð r ì ¢ £�ð  ²©e�b.h)u~}ljsy��h)g�osbs� � r&£°{×A� � q r ��°{×A��©ë~ü`ë¤�©ë ¬�h)g\u{e<g�}lzUokqfe?jky��h)gÊnAo�u{h)b�glhZnAh)b�nlosu�rlq.h)�Au{oszUe#e?g�c.osq.y~h)qs��bdo�cfy~osglo��}lo�u{e?b�jkh)glnly~jsy{h?glosbxnAo�Æxy{q.y~ji¦lu{o�c5y{z|rlu{y~j�e?ga� q r � " r�¢|��� ÷ r ¡�tÅgÉ�h?c.osb.o���}loå1tY¢7zÑ¡4v~r ¡{v���Æxo�z|hZnAh���}lo�b3�h)u~h<� � osbÉ}lg3e�y~glj`�h?�)gly~cfeA�v²©e�okjs}3e?jky��h)gÇe?bdhZjkywe?nle�e?urlqdy{z|osqÈgAhZnlh�okb � t $ � z $ � v:� � rȪet $ � v�x � t $ � z $ ÷ vn� ÷  ºZok�È�}lgÇu{h)bÉj`�e1u{js}Au{h)bÉnlokuBrAq.h)�lu~oszUe�e?g�cfosqdy{h)qe� t $ � z $ � vDr �l�l�Çr�h)qÉuwe�b.y~zUo�cfqs�� e�nlosunly~�l}M·dhh� t $ � z $ ÷ vNr¿� t $ � z $ q v�r x�£)�O�]nlosz��e?beª ì ¢A�ljkh)gÇu{h�js}3e1u.� � r £�°)¡Z�

£�¢�à

Page 114: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�©ë~ü`ëÍ�°ë ²©e?bpÄÅ}lgljky{h)gAosbÉ�3e?bdo%okg�Å q.okb.r�h)glnlokg#e�uwe?bÈÄ1�h?q.z�}lu{e?b$ � rÙtm£òxA�]vTtУ�x lvÐz $ q r��1tУ�x lvÐz $ ÷ r��Il z $ " r�tm£�xA�]v�l  ¬�h)gÇuwe�g�}lz|osq.e?jsy��h)g�nlo*u{h)bȱ��okqdcfy~jsokb]nloYÅ£/¾ tY¢Hzi¢4v ¡}¾ tУ4zi¢�v ×(¾ tУ4z�£vÐz �.¾ t ¢Hz�£vѸ

bdo*c.y{okglo*�K}Ao $ �©±?e1u{o�£%osgÇosu°±��osqmcfy~jso³D¡x��osbdy{z|h���jsosqdhUokg�oku`q.okbdcfhA�²©e�z�e1c.q.y~Ãxnlo*q.y~�)y{nlokÃx��osu°±?osj�cfh)qÉnlo*j�e1q.��e�±)okglnlql�e?g<n3e1nlh)bÉr^h?q� � ëIr �ä tLÔ $ � �1Ô $ ë�o $ � $ ëÍvÄz ¼ � r !ä �Il $ �  

²©e?b5ÄÅ}lgljsy~h)glokbx�3e?bdo�b.o�h?�Acfy~osglokg#}lg3e?b�nlo�h?c.qfe?b]�)y{q.e?glnlhUosuGjk}3e?nlq.e?nlh]Åx�Pu{h���}lookbdcie1�lu{okjso*uwe?bpbdy{z|okc.q��� e1b� �Ì� r¿� qÌq r¿� ÷Ì÷ r¿� "n" z � ��q r¿� q ÷ rÈ� ÷�" rÈ� " � z � � ÷ r¿� q "  a�u`j`�e?u~js}lu~h�nlo*osbmcie?b5j�e?g�c.y{n3e?nAosbÉosbÉb.okgljsy~u{u~hlt� �Ì� r ä � tУ�x lv q oÈtm£òxA�]v q � ë4�âë�lVo ä tm£�xA�]v q tУ�xAlv q ë��wë�l·r ïñ� ��q r ä ��x�t�l.x�£v q o �1tm£ex)�]v � ë4�wë�l±o ä �1tm£�xA�]vTtУ�x lv q ë4�wë�l�r�x £ñ� � ÷ r !ä �ÚtLl�x+£vylVoÈtL�wx�£vy� � ë4�wë�l±o !ä �IlutУòxA�]vTtУex lHv�ë4�âë�l·r x £?£×?Õ»Bh)qÉh?cfq.e�rle?qdc.o

¼ � r !ä �Il $ � r ��c �� �IlutУ�xA�]vTtm£�xAlHv~ë4�âë�l0r £×)Õ¼ q r !ä �Il $ q r ��c �� � q lutУòx lv~ë4�wë�l�r ££�î¼ ÷ r !ä �Il $ ÷ r ��c �� � q l q ë4�wë�l·r £ñ z ¼ " r¹¼ q  ��u{e�bdh)u{}Ajsy��h?g�nlo

ÊËËÌ ï4°{ñ x%£°{ñ x%£)£°*×)Õ x�£°*ñx%£°{ñ ï4°{ñ x�£°*ñ x%£)£°*×)Õx%£)£°{×)Õ x%£°{ñ ï4°{ñ x�£°*ñx%£°{ñ x%£)£°{×?Õ x�£°*ñ ï4°{ñÍ�ÎÎÏ ÊËËÌ � �� q� ÷� "

Í�ÎÎÏ r ÊËËÌ £°{×)Õ£°Z£�{ñ£°Z£�îÍ�ÎÎÏ

£�¢)Õ

Page 115: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

okbK� � r ¢ m ¡)¡Z£à*×A�s�k�s�#� ÷ r ¢ m ¡*ñ4î?��ÕA�k�s�k�#� q r5� " r ¢ m ¡1�l��©ë~ü`ëÍ�°ë ²©e�jsh)gAnly{jky��h)g�nlo�¾*e?u{okq�ç�y{g�okb �� ìhx Æ�qÚåÆ� q x»|·o Æ�åÆ� ð $ � tL�]vNë4��r ¢7 

a�y~g�cfos�?qfe?glnAh|r�h)qpr3e1qdcfokbÉosu°cZ�okq.z|y{glh���}lo%jsh?g�c.y{okglo*uwe�r3e?qdjsy{e?u°b.ok�)}lglnle

�� ì ÆIåÆ�� $ m � o Æ�åÆ� $ � ð ë4��r | $ � ë4�� �]u`b.}lbmcfy~c.}ly{qÂå�t���z¡��v�r « �jëÇt���v $ ëÇt��]v�b.o%u{u~os��e�eB ë �jë �� $ m ë $ m � o B ë � më �� $ ë $ � r | $ �  ÆxoxÄÅh)qdz�e���}lo%uwe1bpz�e1c.q.y~jsosb O � � O q cfy{okglosg�jkh)zUh�oku{osz|osg�c.h)b

� �� ë r �� $ ë $ � � � q� ë r �� $ m ë $ m �qdosb.r�osj�cfyª±?e1zUokg�c.o?��]gAh)b�j`�e1u{js}Au{h)b%z�}A�´b.okgljsy~u{u~h)b�r�osqdzUyªcfosg³nlosnA}ljsy~q���}lo�okgÊosu�oE·dosz|rlu{h���}lo�b.oy~glnly{jse O � ríì ¡{°{ñ £°Z£�K£�î ¡4°{ñeð � O q ríì Õ x/×x3× Õdð  

ÌÎÍ �©ë{ü°ë � ë tÏÓxz|y~c.y{nlh�vÑ�ÌÎÍ �©ë{ü°ëÍ °ë tÏÓxz|y~c.y{nlh�vÑ�ÌÎÍ �©ë{ü°ëÍ&°ë tÏÓxz|y~c.y{nlh�vÑ��©ë¤�Bë ê3ë ²Be\nly~bdcie1gljsy{e\nAoÝu+e�û b.okq3�e X�u�x åxX<nlh?glnlo\å osbÇuweÊrlqdh¥�?osjkjsy��h?gh)qmcfh)�?h)g3e?u^nlo|u�osg�ûU�O»Âe?qfe�j�e?u~js}lu{e?q.u{e�¦3e�����}lo%��}lo*y{z|r^h)gAosq

x uÅx å�zfbdosgò� y r x u.x å�z.b.osgütÏ¡#�]v y r x u�xAå�zfbdosg�t�×*�]v y r ¢£�¢�ï

Page 116: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

jkh)g?åwr « bdosgò��o�\*bdosg�tY¡#�]v�oj��b.okg�t�×*�]vÑ�Kr�h)qd�K}Ao/åd¦ û|��a�z|rlu{ose?glnlh*u{e*h?qdcfh?�)h1�g3e1u{y{nle?n�nlo*b.okg�t N4�]vÈosg)Ü ¢Hz � ÞÏ�Aosbdc.hUy~zUrAu{y{jse« r ¡� ÷� u�bdosg��âë4��r î� z \dr ¡� ÷� u8b.okg�tÏ¡#�]vNë4��r ¢Hz�¥r ¡� ÷� u�bdosg�t�×#�]v�ë4�âr î

¡4ï �  ��u{e�nAy{bdcfe?gljkywe�nlokb.o�e1n3eUokbë�r ì �� t�uÅx « b.okge�?x��Èb.okg�t�×*�]v�v q ë�� ð ����qr ì �� u q x « q �� bdosg q �âë4�¥xi� q �� b.osg q t�×*�]vNë4� ð ����q z

nlh?glnlo*b.o*¦3e�}lbfe1nlhUnAo%g�}lo�±)hUuwe�h)qmcfh)�)h?g3e?u{y~n3e?n°�vºZ}lbmcfy~c.}A�)okglnlhl�ëÅr ì � �×?¢ x ×)¡� x ×�¡ï)¡{ñ � ð ����q r ¢ m ¢�¡{ï4ï?¢A£� j j 

�©ë¤�Bë~ö°ë ºZose?g $ ÷ � $ � � $ � �~�k�s�.u~h)bOcfqfe1b.uwe1n3e?nlh)bOokg�}lg3eZ�Znlh?bs��cfqdosbs�ª�s�k�.}lgAy{n3e?nAosbÈnlo$ � ¸l��b.ose?g $ q � $ " � $ � �ª�s�k�.u~h|z|y{bdzUh�rle?qfe $ q �OÆ�e?n3eh|J¦ µ�ý � Ð ½�þ bdo�eI?tL�]vNr q ½ � �B ë 2 � |~t�$�°)¡4v $ ë�t��]vÄ Óx��±Kywe?z|osg�cfoI`¦éµ�ý � Ð ½�þ ���]nlosz��e?b*osb%Ä1�e?jsy~uvjsh)z|rlqdh)�3e?q*��}loJI¥tL¢ü°)¡4vVrä|~t�¢u°)¡4vr3e1qfe�¢ü°?¡ ¦�Ü ¢Hz�û¶ÞY�Z¢Ý¦�� t r�h)qd�K}Ao $ � tУ°)¡4v�r $ q tУv0r £)� $ � tY¢�v0r $ � tУv0r$ q tm£°?¡4v�r ¢�v�� ��bs�� �K}Ao´okgÔj�e?n3eÊy~g�c.osqm±?e1u{h�Ü N4znNwo £TÞY�GI ��| b.h?gÔÄÅ}Agljsy~h)glosbjk}3e?nlql�e1cfy~j�e?b:��}lo�cfh?z�e?gUosu�zUy~b.z|h%±1e?u~h)qOosg�u~h)b:rl}lg�cfh)b�N���t NÂo\£�v¡°)¡��<NÂo\£?��»Âh)qcfe?g�cfh�nlos��osg�jsh)y~gljsy~nly{qk��©ë¤�Bë~ü°ë �5g3e�±)okÃ|��}lo�okuvrlq.h?�lu{okz�e�e1g�c.osqdy{h)q�e1b.os�?}lqfe���}lo�uwe?b]ÄÅ}lgljsy~h)glokb��3e?b.o�)okglosq.e?g�c.hZnle?bÉuwe?bpÄÅ}lgljky{h)gAosb5js}3e?nAq3�e1c.y{j�e1b]e�cfqdh)Ãsh)bÉnlo�µ ý � Ð ½[þ ���3e?bmcie�jsh)z|rlqdh)�3e?q��}lo�u{e�b.h)u~}ljsy��h)g�åA¦°µ ý � Ð � �iþ �P��e���}lo�r�h)qxokuvu{okz�e�nAo|¬U�o�e�uwe�e1rlq.h�µZy{zUe?jsy��h)g<bdosql�e�h)rZcfy{zUeA�»Âh?q|q.e?Ãsh?glosb|nloÇq.os�?}luwe?qdy{n3e1n°�Oj�e?��o�osb.r�osq.e?q|}lg3e'b.h)u~}ljsy��h)g\�K}Ao�glh´b3�h?u{h'b.osejk}3e?nlql�e1cfy~j�eÇeÇcfqdh)Ãsh?bs�Gbdy{glhÇ��}lo�}Ag3eÇÄ1�h)qdz�}lu{e�nAosuOcfy{r�h�å»r O � q o�^.�âo��×b.ose±��e?u~y{n3e�okgÇc.hZnlh�bd}�nlh?zUy~gly{h�nAo%nAokÁ3gly~jsy��h)g°�:ºZ}lbmcfyªcf}A�?osglnlhUb.o�cfy~osgloxeå m m o¿t��·o £�v�åâr xx¡ O o O �I÷�o�^.� q oP�V��o O � q o�^.��oP�} 

£�¢4î

Page 117: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

®Enlokg�cfy~Álj�e?glnAh�jshKokÁ3jky{okg�c.osbxbdo�h)�Zcfy{okglo(åÛrp� q o £���}lo�jkuwe?q.e?zUokg�cfo%bfe1c.y{bdÄ e1jso%uwe?bjkh)glnly~jsy{h?glosbpnlo*jkh)g�cfh)qdglhl�

£�¢4ñ

Page 118: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

£)£�¢

Page 119: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

� à*ä ßæ\B à�ç�à*ä�ã´à �+à%â <�ß� é

Page 120: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...
Page 121: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

a�bdc.h)bÉq.osb^�}lzUokglosbÉglh�bd}lbdc.y~c.}A�)okg#e�u{h)bÈe?rl}lg�cfokbÉnlosu`jk}lq.bdh|r�osqdh�b��� jsh?gAÄÅh)q.zUe?g}lgle#q.okÄÅokq.okgljsy{e#jsh)z|rlu{o�cie<nAo�cfhKnlh)b�u~h)b�c.oszUe?b�cfq.e1cie1nlh)bs�´ºK}�rAq.h)rÉ�h?b.y~c.h#osb���}lobdy{qd±1e?g'nloUe��K}ln3e<e1u�osbdc.}lnly~h�okg³}lgle�e?bdy{�)gle1cf}lq.e�cie?g´o�µKcfokglbfe�jsh)z|h��osbdcfeA�U»Ge?q.eoku{u{hUosg'j�e1n3e�b.okjsjsy��h)g'b.o�y~glnly{jse?g#okb.js}Aokcie1zUokg�c.o�uwe?b]y{nlose?bxrlqdy{gljky{r3e?u~osb�t uwe1b�r3e?u{eM��lq.e?b�jkuwe�±)o�okbdc��e1g�bdo� g3e?u{e?n3e?b�jsh)gÊu~okc.qfe#y{gAjsu{y~g3e?n3e4v��<�×jkh)g�cfy~gK}le?jsy��h)g>b.o�e� gle?nlosge?u~�)}lglh?b:jkh)z|osg�cie?qdy{h)b:e?jkosqdj�e�nlo5uwe*y{z|r�h)qdcfe?gljsy{exq.okuwe1c.y~±1e�nlo�u~h)bOq.osbd}lu~cfe?nlh)bO��b.}Abqdosuwe1jsy{h?glosbk�Âe1b��� jsh)z|hÇy{glnly~j�e?jky{h)gAosb*e?jkosq.jse�nloUuwe?bxÄ1�h?q.z�}lu{e?b*��}loUokb�jkh)g�±)okgly{okg�c.oz|osz|h)q.y~Ã�e?qk�Â�]u^Á3gle?uPnlo�j�e?n3e�jse?r`�� cf}lu~h�b.o�y{gljku{}A�?ox}lg3e�u~y{bdcfe%jkh)g�u{h?b�g��}lz|osqdh)b�nlou~h)b�rlq.h?�lu{okz�e?b�z+�e?b�qdosrlqdosbdosg�cie1c.y~±?h)b�nAo|u{e?b�jsh?u{osjkjsy~h)glosb*nly~bdc.q.y{�A}ly{n3e1b�e�u{h�uwe1q.�)hnloku�jk}lq.bdhl�&a�g�osu´�}Au~cfy~zUh'jse?r`�� c.}lu{h³b.o#¦le>h)zUyªcfy~nlh'r^h)qUb.okq�b.}AÁ3jky{okg�c.o�jsh)g�u{h)boE·dosz|rlu{h)bȱKy~bdcfh?bposgÇjsuwe1b.o?�� � ��H�p�{�j�Y���j� �a� �j�6�p��U��� �S�������¡ I¢¤£¥£§¦¥¨���

®Enlose?bp��q.okb.}luªcie?nAh)bÉ�É�e?b.y~jsh)b tt ²©h?b�rlq.h?�lu{okz�e?b.l m rg|�tL��z�lHv*jkh)ga|Ë�3e�·dh�}lg3e<n8�ok�ly{u:jsh?glnly{jky��h)g"nlo�q.ok�)}Z�u{e?q.y~n3e?n�cfy~osglokg�bdh)u{}Ajsy��h?g&�}lgAy{j�e�okg<}lgÇr^ok��}lo� glhUosg�cfh)qdglh|}lg3e|±?osÃ%osbdr^okjsy~Álj�e?nlhUosu±1e?u~h)qÈy{gAy{jsy{e?u lut��7vÑ�t »Ge1qfe�q.okb.h)uª±)osq|g�}lz\�osq.y~j�e?z|osg�c.o�osbdc.h)b|rlq.h)�Au{oszUe?b�bdoÇjkh)glbdy{nlokqfe'¦3e?�lyªcf}3e?u �z|osg�cfo�}lgle ��õÍó ¾ ���ô�õM© ¶ ¾ õ#¼� º��Ûrk�I� æ � � æ � q æ ����� æ � ½Ýr;¼�nAoUu~h)bx±1e?u{h)qdosbnloV����b.o%e?rlu~y{jse?g�z\�o�cfhKnlh)bp��}lo�e?rlqdh�µZy~z�e?gâl�tL� � v�r�h)qpjsy~osqdc.h�±?e1u{h)qsl � �¬�h)z|osg�cie1q.y{h?b ta�bdcfe<b.okjsjsy��h)g³c.y{okgloU}Ag>rlq.h?rÉ�h)b.yªcfh�e?}ZµZy{u~ywe?qx�'rAq.osu~y{z|y{g3e1qs��²`hÇz+�e1b�jkh)gljsqdokc.h��}lo�bdo�r^hKnlqs�� eUrAq.osjky{b.e?q�okbx��}lo�uwe"«dn8�os�Ay{uGjkh)glnly~jsy��h)g<nlo�q.os�?}luwe?qdy{n3e1nl¯�okg�uweUy~nlo�ee?g�c.osq.y~h)qposb5²`y{rAb.ji¦lyªcfÃ�osgÇuwe�bdos�)}lgAn3e�±1e?qdywe?�Au{o���jkh)g�cfy~gK}le|okg<e?z��3e?bs�

�U�@ª « ¨¬ �"�¡ O��  ¬�­ ¢O® ¬ �®Enlose?bp��q.okb.}luªcie?nAh)bÉ�É�e?b.y~jsh)b tt a�u � ¼��ô:�j�#� �#�Y¯KÖ,½���� okb�osu8z+�e1b�b.okgljsy~u{u{h�nlo�u~h)b�nlo�}AgÊr3e?b.hA�´ºZo�q.oknl}ljkobdy{z|rlu{okzUokg�c.o�e�e1rlq.h�µZy{zUe?q5uwe�nlokq.yª±?e1n3e�r�h)q�okuGjshKjsy~osg�cfo�y{gljkq.osz|osg�cfe?uÏ��a�b�nlokjsy~qs�bdo%qdy{�)o�r�h)qpu{e�Ä1�h)q.z�}Auwe�l � � � rÈl � oP¯I|~tL� � z�l � vÑ�t ºKoÊnly{jko>��}loÊ}lg�z\�okcfhKnlh+okb�¾ � º ×3���Rí � º ô:� b.y�e+�3e?b.oÊnAo>cfh)zUe?qÇuwe�nly~bm�jkq.okc.y{Ãse?jsy��h)g³bd}AÁ3jky{osg�c.osz|osg�cfo|Á3g3eAt�¯Ar=����� � xã���s¾ ¢�v��'oku�±?e1u{h)q�y~gly{jkywe?uÂz�}A�

£)£�×

Page 122: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

jkosq.jse?glh�e1u^nloku^rAq.h)�lu~oszUe*c.o`�h)qdy{jkhât�l*�D¾ l�tL�I�Ðv�v��Kb.o�h?�Acfy~osglo]�K}Ao�u{h?bDl � okbdc3�e?g�cie?gjkosq.jseUjkh)zUh�bdo���}ly{okqfe�nlo(lut�� � vÑ���]nlosz��e?bÉb.o�nly{jko%��}lo%osb|¾ � º ×3���oí!� º ô:�<�#���3���#� ºÊ bdyvr3e?q.e�rlqdh)�lu{okz�e1b�b.}ZÁ3jsy~osg�cfokzUokg�c.o�q.ok�)}luwe1q.osb�osbdcfe�jsokq.j�e1g`�� e�bdo�rl}loknlo�e?jsh1cie?qbd}lr^okq.y~h)q.z|osg�cfo�osg�}lg�y~g�c.osqm±?e1u{h�r�h)q�e1u{�)hUnlosuÂh)q.nlokg'nlo�uweUr^h?c.osgljkywe Ê �?�osbdy{zUeUnlo¯°�3osbÉnlokjsy~q�XÐlut�� � v�xAl � Xsr¿Æ¥tǯ4Év��t a�u`z\�o�cfhKnlh�nlo%a�}lu{okqÉosbÉjsh)g�±?osq.�?osg�cfo�nlo*h)q.nlokg³£?t ��glh|nlo*h)q.nlokg�zUe��)h)q�v��¬�h)z|osg�cie1q.y{h?b t¹�e��Ç��}lo�jkh)glhKjsokq]nlo�zUokzUh?q.ywe�u{e�Ä1�h?q.z�}lu{e|nAosu©z\�o�cfhKnlh|nlo�a�}lu~osq5r^okq.h�gAh�osbglokjsokbfe?qdy{h*bfe?��osqOu{exjsh?cfe�c.o`�h)qdy{jsexr3e?qfegXÐl�tL� � v7x?l � X���}lo5e?bdos�)}lq.e%bd}�jsh)g�±)okq.�)okgljsy{et ���K}Ao�osb8�3e?bmcie?g�cfo�r^h)�Aq.o5osg�u{e%rAq3�e?j�cfy{jse�v��v­]h�¦le��|��}lo]jsh)gAÄÅ}Aglnly{qdb.o]nlos�ly~nlh�e%uwee?z��ly{�.f}lokn3e?n�jsh?g���}lo�bdox}lbfe�¦3e?�lyªcf}3e?u~zUokg�cfoÉosu�cZ�okq.z|y{glh �Z���!� º �!� ¾ � º ×3���oí!� ºO¾ õ ¶Z�ºZok�È�}lg�u{e5nAokÁ3gly~jsy��h)g°�?u{e5jkh?cie/Æwt�¯ É vBnlok�^o8js}lz|rlu{y~q.bdo:jk}3e?glnAh}|UosbÂb.}AÁljsy{okg�cfosz|osg�c.oqdos�)}lu{e?qs�3u~hU��}lo�glh�oѵZjsu{}Z�)o���}lo�osg�e?u~�È�}lg�j�e?bdh�r3e1qdcfy~js}lu{e?qÉb.o�h)�Acfokgl��e|}lg3eUjkh?ciez|oзdh)qk�Ȭ�h?g<osuBe?�A}lb.hUnlo�gAh?cie?jky��h)gÇh)��±Ky{h|b.o%nly{jko���}lo%osu©h)qdnlosg�nlo%jsh)g�±)okq.�)okgljsy{eokb�zUe��?h)q�rle?qfe<okb.o�rAq.h)�lu~oszUeA��a�gÊosu:b.okg�c.y{nlh<jsh)g�cfq.e?q.y~hl�Gbdo�rl}loknlosgÊokgljsh?g�c.qfe?qoE·dosz|rlu{h)bPjsh)g*r�hZjseÉqdos�)}Auwe?qdy{n3e?n0t r�h)q`oзdokzUrlu~hÈjsh?g�|�glhÉnlyªÄÅosqdosgljkywe?�lu~o�v^nAo�z�e?gAosqfe��}lo*osu`zÊ�okc.hZnAh|nAo�a�}lu~osqpglh�cfokgl��e�b.y~��}ly{okqfe�h)q.nAosgÇ}lglhl�

�U�±° ²��´³ ¨¬ ���¡ O�µ¦�³·¶O®¸¨¹ £§¦±���hº»®�¼_� ¬¾½ ®�¼·  ¬ ®¿����¼À¶ ¬ £§¦��®Enlose?bp��q.okb.}luªcie?nAh)bÉ�É�e?b.y~jsh)b tt ²©eÇqdos�)u{e�nlosu�cfq.e?r�osjsy~h�osb%}lg³zÊ�okc.hZnAhÇnAoUh)qdnlosg³nlo�jsh)g�±?osq.�?osgljkywe�¡�osg´osu��}lo}l � � � gAhUe1r3e?q.okjso*o�µZrluÏ�� jky~cie1zUokg�c.o�nlosbdr^oE·.e?nlhl�¬�h)z|osg�cie1q.y{h?b ta�uÉrlq.h)rp�h)b.yªcfh"nAo�okbdcie´b.okjsjsy��h)g+okb�b.y~zUrAu{osz|osg�c.oÇz|h)bmcfqfe1q|��}loǦ3e���z\�o�cfhKnlh)bz|oзdh)qdosbUosgÔjs}3e1g�c.h\e"h)qdnlosg�r�osqdhÊr^okh)q.okb�osgÔjs}le?g�cfh\e?u5jsh)bmcfo�jkh)zUrA}Acie?jky{h)gle?utÅz+�e?bÉe1nlosu{e?g�cfo�b.o�±?osq3�e���}lo*uwe�osbmcie?�Ay{u{y~n3e?n�okg�cfqfe�cie1z��ly��okg�osgÇosbmcfo%�3e?uwe1gljsojv��O­]h¦3e��Ug3e?n3e�okb.r�osjkywe?u^�K}AoxzUokzUh?q.y{Ãse?q:r^okq.h�glh�jk}losbmcie�gly~gl�È�}lg�okbdÄÅ}lokq.Ãkh|qdosjkh)q.n3e1qÈuweÄ1�h)qdz�}lu{e�nlo%uwe�q.ok�)uwe�nAosu`cfq.e?r^okjsy~hl�

�U�KÁ « ¨¬ �"�¡ O�QÂ�  ¬Äà ¼¥ÅH®��U�®Enlose?bp��q.okb.}luªcie?nAh)bÉ�É�e?b.y~jsh)b tt ²`h)b ��¼�ôn� �!�ór�#�ZÆ ¶<Ç ½��Z� jsh)gAb.y{bmcfokg#osg<c.h)zUe?qpjsh)z|hhl � � � osu©r�h)u{y~glh)z|y{h�nlo�Âe��Zu~h)q5osgJ¯#nlo.lut�� � o�¯Iv5¦3e?bmcie�jky{okqdcfhUh)q.nAosg#okb.jsqdy{�ly~osglnAh¥l�ß � � okg<cZ�okq.z|y{glh?b]nlou{e?bpnlosqdy~±1e?n3e1bpnlo.|#��b.}lbmcfy~c.}A�)okglnlh?lut�� � v�r�h)q�l � �

£)£��

Page 123: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

t ºZoxrl}loknlosg�jkh)glbdos�)}ly~qÈz\�okcfhKnlh)b:nlox�Âe��Ku{h)q8nlo�h)qdnlosg�e1q.�lyªcfqfe1q.ywe1zUokg�c.o5e?u~c.hl�¬�h)z|osg�cie1q.y{h?b t¹�e�����}lo%bfe1�^okq5jkh)glbmcfq.}Ay{qÉz\�o�cfhKnlh)bpnlo*�Âe��Zu~h)qpnlo%h)q.nAosgÇ�3e¥·dhl�Oa�g<jk}3e?g�cfh|b.ooѵle1zUy~glosgUe?u{�?}lglh)bOoзdokzUrAu{h)b�bdo]±)okq3�e%�K}Ao]bdh)g�okg��)okglosq.e?u�z\�o�cfhKnlh)bOz�}A��jkh)bdc.h)b.h)bjkh)zUrA}Acie?jky{h)gle?u{z|osg�cfo�js}3e?gAnlhUoku`rlq.h?�lu{okz�e�okb5z��� gAy{zUe?zUokg�cfo�jkh)z|rlu{oE·dhl�

�U�@È « ¨¬ �"�¡ O�QÂ�  ¬ ¢O�ɶ¤¼�Â"�®Enlose?bp��q.okb.}luªcie?nAh)bÉ�É�e?b.y~jsh)b tt ºZo|u{uwe1z�e?g � ¼�ôn� �#��ó_�!�aÖ º � ¶ ó�� e<e?��}loku{u~h)b*osg"u~h)b%�K}Ao¥l � � � bdo�oѵArAq.osb.eokg�cZ�okq.z|y{glh)b�nlo�¯��ËnAo<u{h?bUn3eMcfh)b|nlosu5r3e?bdhÊe?g�cfokq.y~h)qs�Â� � o¶l � � ºKy/l � � � okbdc3�eoѵArAuÒ�� jky~cfe?zUokg�cfoxnlokb.r�oз.e?nAhUbdo�nly~jso���}lo%b.h)g ��·,�.½p¼Ê ¾ õ�ô:��ó �Z��osgÇj�e?bdhUjkh)g�cfqfe1q.y{hA� õ �J¸�.½p¼Ê ¾ õ�ô:��ó �t ºZoÉu{u{e?zUe ���R���Z�m�#�±ôL��Ö ºO¾�¶ ¾ õ#¼� º°�¢¯ � �Ke�uwe�jse?g�cfy{nle?nU��}lo5¦3e?�Aq��� e���}lo5b.}lzUe?qdu{oe�u{e]okjs}3e?jky��h)g���}lo�nlokÁ3gAop}lg�z\�o�cfhKnlh�nAoÈ}lg�r3e?bdh�r3e?q.e���}lopuweɱ)osqdn3e?nlokqfe�b.h?u{}ljky��h)gu{eUbfeMcfy{bmÁ3jsy~osq.e�b.}lbmcfy~c.}A�)okglnlh�l � r�h)q±l�tL� � v]o�l � � � r�h)q3l�tL� � � � v��*a�g�}lg'z\�okcfhKnlhoѵArAuÒ�� jky~c.hl��osu�osqdq.h)qOnloÉcfqd}lgljse?jsy��h)gUgAh�osb:z��e?bO�K}Ao�osu8«dokq.qdh)qOu{hKj�e?u~¯Vlut�� � � � v�x�l � � �jk}3e?glnlh´b.o�bd}lr^h?glo��K}Ao�okgËokupr3e?b.h´e?g�c.osq.y~h)q�glh´¦3e�¦3e?�ly~nlh'osqdq.h)qk�8okb|nAosjsy~qs�:uweu~uwe?zUe?n3eJË õ��g¼��ô:�Úó�õ�óG�#�M½�� ¾�¶ ½�õs© ¶¢¾ õ#¼� º?l � r¹l�tL� � v��t ºZo%nly{jko%��}lo�}lg<zÊ�okc.hZnAh|okbY¾ � º ó¡õÍójôn� º ô:���#���3���#� º Ê h|��}lo�c.y{okglo �Z���#� º �#�¾ � º ó¡õÍójôn� ºO¾ õ ¶ Ê bdy[¯ � rÈÆ¥tǯ É � � v��t ºZy]}Ag+z\�o�cfhKnlh"okb�jsh?glb.y~bdcfokg�cfo#nlo�h)q.nAosg Ê okg�cfh)gljkosb�okb�jsh)g�±?osq.�?osg�cfo�nloh)qdnlosg Ê t �3e�·dh|jky{okqdcie�n8�ok�ly{uPjsh)glnAy{jsy��h)g�nlo*q.ok�)}luwe1q.y{nle?n���}lo%b.o*n3e�r^h?qpb.}lrl}Aosbdcfe�v��¬�h)z|osg�cie1q.y{h?b tÆxo%gK}Aok±)h�glhUokb�glokjsokbfe?qdy{hUe?rlq.okglnlokq.b.o�osu`cfokh)q.okz�e���}lo�e1jsh?cfe|o�ÄÅosjkc.y~±1e?z|osg�cfoXÐl�tL� � v x¶l � XpokgUcZ�okq.z|y{glh?b:nAosu�osq.qdh)q:nlo5c.q.}lgAj�e?jky��h)g°�H¯U�|e?u~�)}lg3e?b:jsh?glbdcfe?g�cfosbk�:aOby~zUr�h)qdcfe?g�cfo�okg�c.osglnAosq�u{e�nlokÁ3gAy{jsy��h)g´nlo�h)q.nlokg"nlo|jsh?glb.y~bdcfokgljsy{eÇr�h)qd�K}AoUnlokb.nloUosurl}Ag�c.h�nAo5±Ky{bmcie�cfo°�h)q.y~jsh%e?nl��}ly~q.y{ql�e�cfhKnlh%osu3rlqdh?cie?�?h)gly{bdzUhxÄÅqdosg�cfo]e?u3nloÉjkh)g�±)osqd�)osgK�jkyweA�

�U�±Ì « ¨¬ �"�¡ O�QÂ�  ¬ÎÍ ¢O� ½U¬#ÏVÐ ¢h�B�"¼®Enlose?bp��q.okb.}luªcie?nAh)bÉ�É�e?b.y~jsh)b tt ²`h)b ��¼�ôn� �!�óJ�#�|ÑYÖ º í!��¸)Ò�Öô�ô ¶<b.h?g�zÊ�okc.hZnAh)b�nlo�}lg\r3e?bdh�l � � � rgl � o¯ $ t�� � z¡l � z�l � � � ¸Ð¯Iv�nlh)gAnlo�uwe�ÄÅ}lgAjsy��h?g $ okbÉ}lg3e�zUoknlywe�r�h)glnAosqfe1n3e�nlo*uwe�ÄÅ}lgljky��h)g

£)£à

Page 124: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

|ËnAosu�rAq.h)�lu~oszUeÇo�±1e?u{}3e1n3e<osg"rl}lg�cfh)b���}lo�e<b.}>±?osÃ�nlokr^okglnlokg�nAo¥� � �~l � �"nloz|osnly{e?bÈr�h)glnlokqfe?nle?b]nAoÅ|B�:� �e?bÉjsh)gAjsq.o�cie?z|osg�c.o?��b.h)gÇz\�okcfhKnlh)bpnAo%u{e�ÄÅh)q.zUeØ,�]rp|~t�� � o�@��L¯uz�l � o㯠AB ¬ 2 � �C� ¬ Ø ¬ vÄz D�r&£4zÑ¡7zT j j Äz�El � � � rÈl � o㯠AB ¬ 2 � ¼ ¬ Ø ¬  t �]g�z\�okc.hZnlh�nlo(®É}lgl�)oÑ�:9�}Acdcie�b.o*q.okrlq.okb.okg�cfe�r�h)qpb.} ô ¶�Ó ½}�������#�HÔrÖô ¾ÕË ���@ � � �Ì� � ��q  j j  � � A@ q � q¡� � qÌq  j j  � q A��� ��� ��� � � � ���@ A � A � � A q  j j  � AiA¼ � ¼ q  j j  ¼ A��bdo*nly{jko%��}lo�E�okbÉosu�º ¼Ö,�]�����_�#�³�ô ¶ � ¶ ó �t �5g�z\�o�cfhKnlh�nAoò®5}Agl�)o��n9�}Ac.cfe�osb�oѵArAuÒ�� jky~c.h�js}le?glnlh}�C� ¬ r ¢�r3e?q.e�cfhKnlhsNJæ�D��okbÉy{z|rluÒ�� jsy~c.h�okg�jse?b.h|jsh)g�c.qfe?qdy{hl�

¬�h)z|osg�cie1q.y{h?b ta�b�glokjsokbfe?qdy{h»t �³z�}A�´b.osgAjsy{u~u{h�vxb.e?�^okq�rle?bfe?q�nlo�}Ag>z\�o�cfhKnlh�e<b.}"cfe?�lu~osq.h��±Ky{jkok±?osq.b.eA�´²`h)b�cie1�lu{okq.h)b�h<Ä1�h)q.z�}luwe?b%jsh?q.q.okb.r�h)glnly~osg�cfokb�e<u{h?b�z\�okcfhKnlh)b�jsu��e?b.y~jsh)bjkh)zUh%osu�nlo]a�}lu{okq�z|oзdh)q.e?nlh*�|aO}Au{osq:z|hZnlyªÁ3j�e1nlh�gAh�osb8glosjkosb.e?q.y~h�z|osz|h)q.y~Ã�e?qdu{h)bk��U�@Ö ×»���¤ I¦�£§¦Õ�Q� ¬ Âw  ¬ �Q��  ¬ �

®Enlose?bp��q.okb.}luªcie?nAh)bÉ�É�e?b.y~jsh)b tt �]g3e�¦Ay{rÉ�h?c.osbdy{b5g3e1cf}Aqfe?uBjsh)gAb.y{nAosqfe1n3e�r�h)qr9�}AcdcieUokbxuwe]¾ � º ��õ ¾ õ#¼� º �#�}ó�Ö,� ¶���Z�¿Ø#½ ¶ ó @��Vr « A¬ 2 � �C� ¬ ��}lo�bdoÇnle?q3�e#r�h)q�b.}Arl}losbmcfh´osg\u{h�bd}ljsokb.yª±)hl�>�Âe?z��Ay��osgbdo�b.}lr�h)glnAq3�e<r3e1qfe<bdy{z|rlu{yªÁ3j�e?q*u{e?b�nAosz|h)bdc.qfe?jky{h)glokbs����}lo�bdo�cfq.e1cieÇjsh)gÊbdy{bmcfoszUe?be?}Zc��h)glh?zUh)bVt�l�mrÈ|~t�lHv¡vÑ�Ar�osqdhUokbdcfh|glh�jsh?glbdc.y~cf}Z�)o%}lg3e�q.osbmcfqdy{jsjky��h)g�okb.osgAjsywe1uÏ�t �]uvnlosb.e?q.qdh)u{u{e?q�r�h)qx�Âe��Ku{h)q�okg)¯'uwe�Ä1�h)qdz�}lu{e�r3e?q.e�osu�osqdq.h)q�nlo�cfq.}Aglj�e?jky��h)gbdo�h)�Zcfy{okgloÇ�K}Ao�u{e´nlo�Á3gly~jsy��h?gËnloÇh)qdnlosgpt nloÇjsh)gAb.y{bmcfokgljsy{e�v�r3e?qfe Ê r £?�É¡��a×bdo�cfq.e?nl}ljko�okg<b.okgln3e?b�osjs}le?jsy~h)glosb]��}lo�y~g�±?h)u{}Ajsqfe1g<u{h?b]oku{osz|osg�c.h)b]nAosu©cie?�lu~osqdhUnloá�}Zcfji¦lokqs�£)£�Õ

Page 125: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

¬�h)z|osg�cie1q.y{h?b ta�bÂz�}A��jsh?g�±?osgly~osg�cfo�osg�cfokglnlosqÂ�ly{okg�oku�e?q.�?}lzUokg�cfh5�K}Ao8u~u{ok±1epeÉuwe?b©jkh)glnly~jsy{h?glosbnlo8h)q.nAosg�e?uKzUokglh)bÂosg�u{h?bGj�e1b.h)bÈ£:��¡K�G��}Agl��}lopglhxokbGcfh?cfe?u{z|osg�c.o8y~zUrlqdosbdjsy{gAnly{�lu~oe?rAq.osgAnlosqdb.o*uwe?b8osjk}3e?jsy~h)glokbp�K}Ao�nlokÁ3gAosgÇosbdcfe?bpjsh?glnly{jky{h)gAosb�nAo�h)q.nlokg�r^h)qd��}loxb.h?gjkh)glb.okjs}lokgljsy{eÇnAo�uwe�cfokh)qs�� e��)okglosq.e?uvnlo�u~h)b'�e?qd�^h)u~osbxnAo?á8}Acfji¦lokqs�©osb�r�hKjsh�jsqdo)�� �lu{o��}lo�nlokb.rl}8�osbÇnlo�r3e?b.e?q�r�h)q�osu�js}lqdb.h\}lglh\b.oseÊj�e?r3e1Ã�nlo�h)u~±Ky~n3e?q|uwe?b�Ä1�h?q.z�}lu{e?b« ¼ ¬ r £��Ç¡ « ¼ ¬ @ ¬ r £)��U�±Ù ¨Ú �EÛ6��® ¬ Â}  ¬�Ü ¢h��£1Ý ¬ �

®Enlose?bp��q.okb.}luªcie?nAh)bÉ�É�e?b.y~jsh)b tÞ �]g ¼¶ � Ó �Z½ ¾ � º � ¶ ¼Ê © okb�}lg>�)q.e1ÄÅh#��}lo�r�hZnAosz|h)b�okg�c.osglnAosq���}lo�q.okrlq.okb.okg�cfe}lg��e1q.��h)uÂ�?osglose?u��h)�?y{jshUnlh)glnAo�uwe�q.el�� Ã%jsh?q.q.okb.r�h)glnlo�e1uve?g�cfokjsokb.h)q�jkh)z �}lg�nlo�c.hZn3eu{e�okbdc.y{q.r�o?�UºZyObdo|nAy{bdc.y{gl�?}lo|eÇu~h)b ×~¼���jô�õ ¾ �Úó t y{gAnly~±Ky{nA}lh)bÚv5jsh)g³glh)z��lqdosb*nly~bdcfy~g�cfh)bbdo�nly{jko���}lo�osu��e?q.��h)uBosbdc3�e�okcfy~��}lokcfe?nlhl�%a�uGh)qdnlosg'nlo�}lg �e?q.��h)uBosb�b.}�g��}AzUokq.h�nlo±��osqmcfy~jsosb.tÅnlo*y{glnlyª±Ky{nl}lh?bpnlo*uwe�osbmcfy~q.r�o�v��Þ ²©e�ÄÅ}lgljky��h)g � ¶ � ��� ��}lo�e1b.y{�?g3e�e�j�e?n3e�glh)z��lq.o1�`o�µZjsokrAcfh<e?uvnlo�uwe�q.el�� Ã1�`osuglh?z��lq.opnAopb.}�r3e?nlqdoposbmc��e�nlokÁlgly{n3e�}lg°�� ±)hKj�e1zUokg�c.o(t jse?n3e�y{glnAy~±Ky{nl}Ah�cfy~osgloÈ}AgUbdh)u{hr3e1nlq.ojv���ºKy{g"okz��3e?qd�)h#e1u�e?bdy{�)gle?q�eÇj�e?nle<glh)z��Aq.o�oku�nloUb.}ʦly ·dh�gAh#b.o�h?�Acfy~osglo}lgle|ÄÅ}lgljky��h)g��ly{okg<nlo�Á3gly~n3e�r�h)q.��}lo�eU±)okjsokbxosbmc��e�z�}Au~cfyª±1e?u{}3e1n3e�t jse?n3eUy~glnlyª±Zy~nl}lhrl}Aosnlo�cfokglosqp±1e?qdy{h)bȦAy ·dh)b�v8��e�±)osjkosb5glh�nlokÁlgly{n3e¶tÅ}lg�y~glnlyª±Zy~nl}lh�rA}losnlo%glh�cfokglosqgly~gl���}lg�¦ly ·dh�v��Þ ¹]e���nlh)bÈÄÅ}Agljsy~h)glosbpz�}A��y~zUr�h)qmcie?g�cfokbpe?bdhZjkywe?n3e1bÈe�}lg �e?qd�^h)u^osg�osux�e?z��lyªcfhnlo*u~h)bpz\�o�cfhKnlh)bpnlo(®É}lgl�)oÑ�:9�}AcdcieAt�в©e]ÄÅ}Agljsy��h)g<�Ue?b.y~�)g3e]e�j�e?nle'�e?q.��h)uKosuKrlq.hKnl}lj�cfh�nloÈu~h)b��h)q.nlokglosb�nAoÈu{h)b��e?qd�^h)u~osb��}lo'±1e?g ��}lokn3e?glnAh�e?u�osu~y{z|y{g3e1q�uweÊq.el�� Ã���qdosr�okcfy~q�osu*rlq.hKjsokb.hËjsh)g u{h �e?qd�^h)u~osbqdosb.}Au~cie1g�c.osbk��:ºKo�e O }Ag�z�e1c.q.y~ÃrE3£aE)�O­5h)z��lq.e?glnlh�u~h)b8±��okqdcfy~jsokbÈnlosux�e?q.��h)u�nly{bmcfy~g�c.h)b�nAoxuweq.el�� Ã8jsh)g�u{e?bGo�cfy{��}lo�cie?bNØ]z�$Ìz���zZ¢0 j j G��uwe�q.el�� Ã8jsh)z|hsN3�)bdoÈjsh)gAb.y{nAosqfexokulrlqdhZnl}Ajkcfh� ­ ß � � � � ­ ß ë � ë � ­ ß`¿ � ¿  T j �nlh)glnAo��6t}DÌv�y~glnly~j�e�osuGr3e?nlqdo�nlo_D.��²Be�ÄÅ}lgAjsy��h?g $ ¬ e1b.y{�?g3e�e?u�e?qd�^h?u°uwe�bd}lz�e�nlo%osbmcfh)bÉrlqdhZnA}ljkc.h)bÉjs}3e?gAnlhwØ z�$Ìz���zD¢0 T j È±1e?q��� e?g�osg�cfqdo|£*��E)�Þ ºZo�jk}lzUrAu{o�oku ô:�p�Z����� ¶ �#�-ÔrÖHô ¾ÕË ��� t%�]g'z\�okcfhKnlh�nloh®É}lgl�)oÑ�:9�}Acdcie�osb*nloh)qdnlosg Ê b.y°��bl�h)u{h�bdy`b.o*js}lz|rlu~o � AB ¬ 2 � ¼ ¬ $ ¬ r�£r3e1qfe�cfhKnlh)b�u{h)b'�e1q.��h)u{okbxnlo�h)qdnlosg'z|osglh)q�hÇy~�)}3e?uB��}lo Ê �°nlh?glnlo�u{h)b3¼ ¬ �#u~h)bV�Câ A£)£ï

Page 126: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

}lb.e?nlh)b5r3e?q.e|jkh)z|rlq.h)�le?qÉuwe�y{�)}le?u{n3e1n�e1g�c.osqdy{h)qpbdh)g<u~h)bÉn3e?nlh)b5r�h)qÉosu`cie?�Au{osqdh�nlosuz\�okc.hZnlhA�Þ Æ�e?nlh�}lg�rlq.h?�lu{okz�e0l�mr¿|~t�lHv8��}lg �e?q.��h)u`js}Z��eUq.el�� Ã�okbdc3�eUokc.y{��}lo�cie?n3e�jsh?g+ ��osuÉq.okbdcfh"nlo�u~h)b�±O�okqdc.y{jsokb�jkh)géø�z¶ªòz��ÈzÛû� T j Ubdo<jkh)glb.y~nlosq.e³oku]rlqdhZnA}lj��c.hJ| �­ � � ß �j� | !­ � � ß ! � | ­ � � ß {�  j j �nlh)glnAo¥� � �Tt��7v%y~glnly~j�e�u~h)b%¦ly ·dh)b�nlo¥�ãt rA}losnlokgÊb.okq�osujkh)gM·d}lg�cfh�±1e?j?�� h�v��UºZo|u{u{e?zUe ��õ Õ ����� ºO¾ õ ¶ ½ ��½����]� º ô ¶ ½ eÇu{e�b.}lzUeÇnAoUu~h)b�rlq.hKnl}lj�cfh)bjkh)q.qdosb.r�h)glnAy{osg�c.osb�jk}3e?glnlh ø�zŪòz��ÈzÅû� j j %±?e1q��� e�osg�c.q.o<£|��ë»t osu:g��}lz|osqdh�nlo±1e?qdywe?�lu~osbOnlo±|uv��|bdo�jsh?g�±Ky~osglox��}lo]u{h)b:b.}Ar^okq��� gAnly{jkosb�y~glnly~j�e?gUosu�gx�}lz|osq.h�nlo�jkhZh?qm�nlokg3e?n3e�nlo.|<��u{h?bpb.}l�°�� glnly~jsosbÉu{e?bȱ1e?q.y{e?�lu{okbÈjsh?g�qdosb.r�osj�cfh�e�u{e?bp��}lo*b.o%nlosqdy~±1e?g°�¬�h)z|osg�cie1q.y{h?b ta�u�cfokh)q.okz�e³nloJá�}Ac.ji¦losq�okb�}lgÔq.osbd}lu~cfe?nlhÊjkosg�cfq.e?uxnlokuxjs}lqdb.h\��}lo�¦3e��+��}lob.e?�^okq5e?rlu{y~j�e?qÈ��zUokzUh)qdy{Ãse?qÈy{gAo�µZjs}lb.e?�lu~osz|osg�cfo1�Èa�bdc.h�y{gAjsu{}Z�)o*uwe?bÉnlo�Á3gly~jsy{h?glosbp�j°�e?u{jk}lu{h)b�nlo $ ¬ �#nlo_�Â��®EgAjsu{}Ab.h�b.y�}lgAhÇgAhÇ��}ly~osqdo|z|osz|h)qdy{Ã�e1q�uwe�nAokÁ3gly~jsy��h)g'nlosunlyªÄÅosqdosgljkywe?u�oku{osz|osg�cfe?uÏ�`��}loUosb%y{z|r^h)qmcie?g�c.o�nlosbdnlo�oku:rA}lg�cfh<nAo|±Ky{bmcie�cfo°�h)q.y~jshl�Âe?uz|osglh?b]nlok�^o�b.okq�j�e1r3e?Ã%nlo�y~g�c.osqdrlq.o�cie?qduwe�jsh)qdq.okjkcie1zUokg�c.o�e?u`±?osq.u{eUokb.jsqdy~cfeA�^u~hU��}loy~zUrlu~y{jse�jsh?glhZjkosqÉuwe�glh1cie?jky��h)g�okzUrlu~o�e?nleA�

�U�±ß à ¬ ³_�QÂS����¼�£§¦¥¨�Q�á  ¬ ®��QÂ�� ¬ �U� ¬ ³_¼�Âw  ¬�Ü ¢h��£1Ý ¬ �®Enlose?bp��q.okb.}luªcie?nAh)bÉ�É�e?b.y~jsh)b tÞ »Ge?q.e�rlq.h?�3e?qr¯ � r�Æ¥tǯ É � � vpb.o�nlokbfe?qdq.h)u~uwe¯ � r�h)q5�Ge��Ku{h?q0t okgJ¯Iv��^u{h���}lookg�u{h?b:zÊ�okc.hZnAh)bOnlo3®É}lgl�?o��:9�}Acdcie*jsh)gAu{u{o�±1e�e?rAu{y{jse?jsy~h)glokb�b.}ljkosb.yª±1e?b�nlo5uwe*q.ok�)uwe�nlou{e|jse?nlosgle���}lo�b.o�rl}loknlosg#c.qfe?nl}Ajsy{q5osg<osu©u{okgl�)}3e¥·do�nlo�u~h)b<�e?q.��h)u{okbÉjsh)g<Ä1�h?q.z�}lu{e?bjkh)zUh�u{e�nlo%§�e��e�nAyüá�q.}Aglh¬�h)z|osg�cie1q.y{h?b t§3}losq.e�nlo�uwe�y~nlo�e��)okglosq.e?uvz|osgljky{h)gle?n3eA�°okbdcfe�bdosjkjsy��h?g´okb*h)r^jky{h)gle?uÏ���#b3�h?u{h�b.oqdosjsh?zUy~osgln3e*jsh?zUh�}lg3e�bdos�)}Agln3e�u~osjkc.}lqfe%r3e?q.e�u{h?b8e1u{}lz|glh)bOy{g�c.osq.okbfe?nAh)bs�:­#�h1cfosbdo?�glhÇh)�lbmcie?g�c.o?�v��}lo|u{h)b*rlqdh)�lu~oszUe?b*rlq.h)rA}losbmcfh)b�osg"okbdcfe�b.okjsjky��h)g³b.h)g³}lg3e�rAq.h)u~h)gZ���e1jsy��h?g�nlo*u{h)bpu{e|e1g�c.osqdy{h)q��?�3r^h?qÉcfe?g�cfhl�ZcfhKn3e�±^�� e�e?jsh)gAb.oз.e1�lu{okbs�

�U���¾â « ¨¬ ���¡ O�U ¬ ã ¶O®¸¨¹ £§¦±���U ��ä���  ¬ �å�QÛh� ¬ �O¦ÕÛO® ¬®Enlose?bp��q.okb.}luªcie?nAh)bÉ�É�e?b.y~jsh)b tÞ a�g<}lgÇz\�o�cfhKnlh|nloÅ®É}lgl�?o��:9�}Acdcie�o�µZrluÏ�� jsyªcfh�osu©h)qdnlosg�glh|rl}losnAo�b.}Ar^okqfe?q5osug��}lz|osqdh�nlo*okcfe?r3e?bk�

£)£�î

Page 127: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

Þ ºZyp}Ag�zÊ�okc.hZnAh�nlo¶®5}lgA�)o��n9*}Zc.cie�oѵArAuÒ�� jky~c.h<cfy~osglo�h)qdnlosg Ê æ`ï#osg�cfh?gljsokbc.y{osgAo�z+�e?bpnAo Ê oÔ£�o�cie?r3e1bs�l��bdy Ê æ�î�osg�c.h)gljsokb]c.y{osgAo�z+�e?bpnAo Ê oË¡�o�cie?r3e1bs�¬�h)z|osg�cie1q.y{h?b tÆxo�u~h)b�nlh?b�q.osbd}lu~cfe?nlh)bxe?g�cfosqdy{h)qdosb�e1g�c.osb�z|osgljky{h)gle?nlh)bk�°�3e?bmcie�Ä e?z|y{u~ywe?qdy{Ã�e1q.b.ojkh)g�oku`rlq.y~zUokq.h���bdosqÉj�e?rle?Ã�nAo%nAosnl}ljky{qdu{h�jsh)z|h�}lg3e�b.y~zUrlu~oxjsh?glb.okjs}lokgljsy{eUnlo%uwec.osh)qs�� e�nlo*u{h?bÇ�e?q.��h)u{okbpnlo(á�}Ac.ji¦losqk�

�U���U� ­ Âc��¦Õ³·¼�£§¦���� ¬ Âæ  ¬�¬ �����Q�®Enlose?bp��q.okb.}luªcie?nAh)bÉ�É�e?b.y~jsh)b tÞ a�u`cZ�osqdzUy~glh�rlqdy{gljky{r3e?u`nAosu`osqdq.h)qÉnlo*cfqd}lgljse?jsy��h)g�nAo�}lgÇz\�okcfhKnlh�nlo%h)q.nAosg ÊokbZ¯ É � � z�}luªcfy~rlu{y~j�e?nlh5r�h)q�}lg�jshKokÁ3jky{okg�c.oÉ�K}Aopb.oÉo�µZrlqdosbfe*jsh?zUh�}lgle*jkh)z��ly~g3e?jky��h)gu~y{glose?uZnAopu{h)bvrAq.hKnl}ljkc.h)b�nlo�£ux��³«í¼ ¬ $ ¬ r�h)qvokulnly~ÄÅokq.okgljsy{e?uAoku{osz|osg�cfe?uAr3e1qfexcfhKnlh)bu~h)bÇ�e?q.��h)u~osbÈnlo%h)qdnlosg Ê o £)�Þ ºZyÉosbmcfo�jshKokÁ3jky{osg�c.o�bdo<e?g�}lu{e´rle?qfe'}lg�rAq.h)�lu~oszUe�r3e?qdc.y{jk}luwe?qk�OosupcZ�okq.z|y{glhrlqdy{gljky{r3e1uPnloE·.e|nlo*bdosq.u~h���osu`h)qdnlosgÇosbÉzUe��)h)qÉnlo*u{h�okb.r�osq.e?nlhl�¬�h)z|osg�cie1q.y{h?b tÆ�e?n3eÇuwe�Ä1�h)q.z�}luwe�r3e?q.e�osuOcZ�okq.z|y{glhÇrlqdy{gljky{r3e?uOnloku8okq.qdh)q�nAoUcfqd}lgljse?jsy��h)g�t ��}loglhUosbxgAosjsokbfe?qdy{h�z|osz|h)qdy{Ã�e1qÚv�¦3e��Ç��}lo�bfe1�^okqxe?rlu~y{jse?q.u{e�e�}lg#rlqdh)�lu~oszUe|jkh)gljsqdokc.hbdosgljky{u{u~hl�va�bmcie�b.okjsjsy��h)g�z�}lokbdcfq.e�jsuwe1qfe?z|osg�cfo�uwe�e?z��ly{�.f}lokn3e?n��)e�b.o� g3e1uwe?n3e�e?uPokz��rlu~o�e?q�oku3cZ�osqdzUy~glh �Z���!� º°tÂosu3cfokh)q.okz�e*nloeá�}Ac.ji¦losq8rluwe?g�c.o�e*jsh)glnAy{jsy~h)glokb:gAosjsokbfe?qdywe?b�³b.}AÁljsy{okg�cfosb�rle?qfe<��}lo�}AgÊz\�o�cfhKnlh<bdo�e#nlo�h?q.nlokg Ê jsh)gÊu{e�nlo�Á3gly{jky��h)g"h)q.y~�)y{g3e1utÅr3e?qfeÉcfhKnlhxrlqdh)�lu~oszUe5bd}AÁ3jsy~osg�cfokzUokg�cfopq.ok�)}lu{e?qÚvÑ�?r�osq.h]b.yZglhxb.o�js}lz|rlu{okg°�?okuZh?q.nlokgrl}Aosnlo%b.ok�)}ly{qpbdy{okglnlh Ê bdy`b.o*q.okbdc.q.y{gA�)o*uwe�nlo�Á3gly{jky��h)gÇe�}lgÇrlq.h)�Au{oszUe�r3e?qmcfy~js}lu{e?qs�

�U����ª ­Nã ����¼À¶-��®�¼�£§¦§¨�Q�ç  ¬ÎÍ ¦�£1ݤ¼��� OÂ"�Q�®Enlose?bp��q.okb.}luªcie?nAh)bÉ�É�e?b.y~jsh)b tÞ ºKy O t�¯ vBosb�}lg3e�e1rlq.h�µZy{zUe?jsy��h)g�nAoph)q.nlokg·¸<nloK^��?osg�osulbdosg�cfy~nlh�nlop��}loK^�rO tǯIv{oâ�.¯ � oâÆ¥tǯ � � ��v���okg�cfh)gljkosb:osuO«mosq.qdh)q.¯³^�x O tǯIvvosb�� O t�¯ v�x O tÏ¡4¯Iv � °tY¡ � x£vIoAÆ¥tǯ � � ��v��vaObmcie�y{nAo�e�bdoxrl}loknlo*e?rlu~y{j�e1q8r3e1qfe�osbmcfy~z�e?q8osu^osq.qdh)qÈnlo]cfq.}Aglj�e?jky��h)gtÅ�K}Ao%okb�«mu{hKj�e?u~¯�v���osu`osqdq.h)qÉ�)u~h)�3e?uY�¬�h)z|osg�cie1q.y{h?b t²©e�y{nAo�ex��}loÈjkh)glnl}ljkoÉexuweÉÄ1�h)q.z�}Auwe]��}lopbd}lbdc.osg�cie�u{e]o�µKc.qfe?r�h)uwe1jsy��h?g�nloò®Éy{ji¦3e1qm�nlbdh)g�osbÉb.}ZÁ3jsy~osg�cfokzUokg�c.o�bdosgljky{u~uwe�r3e?q.e��K}Ao%}Aglh�b.o�e�jse?r3e?Ã*nlo*y{z|rlqdh¥±Ky~bfe?qduweA�Âa�g

£)£�ñ

Page 128: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

u~h)b�e?rl}Ag�c.osb:b.oɦ3e?jkoÉ}lg|e?gÉ�e?u~y{b.y~bvjs}Ay{n3e?nAh)b.hl����}loÉokgUokbdcfoÉjk}lq.bdh�bdo5rA}losnlo5jsh?glb.y~nlo��q.e?q8h?r^jky{h)g3e1uÏ��nlo5j`�h)z|h�bdoxe?rAu{y{jse%u{e%oѵKcfqfe1r^h)u{e?jsy��h)g�nlo±®Éy{ji¦le?q.nlbdh)g�e?u�okbdcf}Anly{h�nlosuokq.q.h?q%nAo�c.q.}lgAj�e?jky��h)g°�U»Âh?q�h?c.qfe�r3e?qmcfo1�Âu{e�okbdc.y{zUe?jsy��h)g'nlosu�h)qdnlosg³osz|r`�� qdy{jkh�r3e?qfez\�okc.hZnlh?bÂnlo8r3e?bdh�Á1·dhl�1�K}AoÈosg�jkuwe?bdo8bdo�±Ky{h]nlosg�cfqdhxnlo8osbdcfe�b.okjsjky��h)g°�?osg�u~h)bGe1rl}lg�cfokbbdo%z|osgAjsy{h?g3e��lq.o�±)osz|osg�c.o�okg�u{e�bdosjkjsy��h?g³£)�ª£àZ��U���p° ×è¼À³ÄÛO¦Õ��  ¬ ¶¤¼�ÂB�

®Enlose?bp��q.okb.}luªcie?nAh)bÉ�É�e?b.y~jsh)b tÞ a�bUz�}lji¦lh"z��e?b�jsh?g�±?osgly~osg�cfo�glh"zUe?g�cfokglosq�Á1·dh´osupcfe?z�e� gAh�nlosuÉr3e?bdhl�ò¯°�¦3e1jsy��okglnlh)u~h�±1e?q.y{e?q�okgÇÄÅ}lgAjsy��h?gÇnAosu°okq.q.h?qp�K}Ao�bdo%okbdc.y{zUe��K}Ao%bdo*osbdc3�e�jsh)z|okc.y{osgAnlhl�Þ a�g�}lg�z\�okcfhKnlh�nAo�h)q.nlokg Ê b.y°okg�jsy{okqdc.h�� � b.o�okbdcfy~z�e��K}Ao�osu°okq.q.h?q�«du{hKj�e1u{¯jkh)zUo�cfy~nlh�osbQP2éÕê�ë���bd}lr�osqfe%e?ulokq.qdh)q�cfh)u~osqfe1nlhJP:ëÕì@í��Kokg�cfh)gljkosb:uwe�u{h?gl�)y~c.}ln�nloku3r3e?bdhbdo|nAos��oUqdosnl}ljky{q�okg³}lg'Ä e?j�cfh)q�nlo|e?u�z|osgAh)bht)P:ëÕì@íÄ°2P2éÕê�ë6vÚ���Rß É � � � �©q.okrly~c.y��okglnlh)bdo�u{h)bj°�e?u{jk}lu{h)bÂnloÈu{e³�}lu~c.y{zUe5yªcfokqfe?jky��h)g°�Ba�bdc.opzUy~b.z|h]Ä e?j�cfh)qÂb.y~qd±)oprle?qfexe1}lzUokg�cie?qÂuwe�u~h)gZ��)yªcf}lnUnlosu^r3e?bdh�b.yPokuPokq.q.h?q�osbmcfy~z�e?nAh�ÄÅ}lokqfe�nlokz�e1b.ywe1nlh�r�os��}lo� glh�osg�jsh?zUr3e1qfe?jky��h)gjkh)g�oku°cfh)u~osq.e?nlhl�¬�h)z|osg�cie1q.y{h?b t²©e�Ä1�h)q.z�}Auwe�r3e1qfe�uwe�qdosnl}Ajsjsy��h)g´nlosuvrle?b.h�osb*}lgle�bdy{z|rlu{o�jsh)glbdosjk}losgljkywe�nlo�uwee?rAq.h�µZy{zUe?jsy��h)g}�ů É � � r3e?qfeÉosu�okq.q.h?qBnAo:c.q.}lgljse?jsy��h)g%�K}Ao8rl}Aosnlo:y{g�cfokq.rlqdokcfe?q.bdo8jkh)zUhe?bdhZjkywe?nAhUe1uBokq.qdh)qÉjsh)z|okc.y{nlh�osg�j�e?nleUr3e?bdhl�È�]b��� �ů É � � ¡ P2éÕê�ë¥� �¥t�¯ m v É � � ¡ P:ëÕì@íî ¯ m r¿¯�t)P:ëÕì@íÄ°2P2éÕê�ë6v ���Rß É � � � �G²Bexy~g�cfq.hKnl}ljkjsy��h)g�nlop}lg�Ä e?j�cfh)qGnlopb.ok�)}lq.y~n3e?n�okb�z�}A�g3eMcf}lq.e?u°r3e?q.e�glhUokbdcfe?qÉosgÇosu`uÏ�� zUyªcfo5nlo*uwe?bÉe1rlq.h�µZy{zUe?jsy~h)glokbs�

�U���§Á ïð¼�� ¬  ¬ �¤£¥¼¾ñc¼� O�UÂò@ó�ô5õ:öø÷,ù�ôúö�û�üþýÿõ:ó��2ö����õ:ö�����2ö Þ��� � ¶ ��� ºO¾�¶���¶ �#� ö�� ó��2ö����ôúý��Bó��2ö¤ó�ô0®¡û �� ô��:9Oû"ý�ýÿõ��Sû�ô��������õVù�ý ô ü�õ�|õVý ù�� � O t�÷!�"�2ù�ý õ ý#� \@6v�ô ö�û¿ýÿõ$��üMôúù���%Vó�ô&�|õ ô5ù�õ'�Sû�ôøû �Hý ô �� õ(�2ù�ó�ô �|õ�÷)�2ù�Sû�ôIô5ü*�Vý ù���+Þ�, õ ó��.-�ô5ù�ô ����õZô ý�ù�ô=ü �:ö'/Võ:ü �:ù�ô5ö0�)�"ý ô �Mó��2ö(�� õ��1�"�2ö(�2�ôúý#�có��2öHö�ô¿ý#���Zõ���)���8ôúö�ý�� �|õ���3�� ó�ô5ü§ôúù�ù��:ù ÷,ö�ô4��õ$�1����õ8ôúü*��õ:ö������ ö�ô��5û�ô ý ô�Yô ý�ô�+

5 �)�Yô ýÿõVù�� �:ö , �2ö6��õ:ù�ô5ö�ô ��õ87�õVó��2ö �Iö�� �6û"÷!�"ù���-�û ó��2ö�ó�ôúö�ó�ô¡ô5ü���û ý#�Ió�ô&/9�MöÕýÿõHý�ô*��2ù�� ��

�1ô5ù��:��� öÕý#�sý�û"÷2ô ü��2ö1�Yô;7��2ù�ô5ö<�2�ôúý#�có��2ö8ô �6û��>=�õ:ö=ö��þý û�õ$�� � ô5ö<��õVù õaù�ôúö��2ü./2ô5ù?8@�A

Page 129: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

û��2�ô5ù�� ��õ$�|ô ý�ôøô�úû�õ����� ôúöQó��.-�ô5ù�ô ����õ:üsô5ö6�2ù�ó�� õVù���õVö%)�"�2ù�ô5üsü �OôúöB������ù�ô5ö��� ó�� ��üsô��� �9�5ô5ù��SûB�ôIö�� ÷C�D��)�E�Yö�ôIô�E��üMô5õ +

�U����È à�¦�¼ ½ ��¼À³_¼�Âæ  ¬�¬GF £§¦ ¬ �¤£§¦Õ¼ò@ó�ô5õ:öø÷,ù�ôúö�û�üþýÿõ:ó��2ö����õ:ö�����2ö ÞIH6 û �2�ô<ý#�có��Ió�ô���õ:ö��KJ$7��Jô5üL�2ù�ó�ô % Ê %Sö�ô���û�ôúó�ôHôúö�ý�� �|õ:ù�ô�E�*�M ù�� �5õ��|ô ý ôû"ý��Mü�� ��õ ó��1�Sû�ôIô5ü¥ü�� � õ:ù��sý����-ó�ô5ü¥ôúù�ù��:ùFôúöFõ���ù��3NO� �|õ:ó�õ$�|ô ý�ô¤û õ<-�û ���P�� ü�� ô5õ:üó�ôúü"ü�� � õ:ù��sý#�E�¡ó�ô�¯1�� �3ô ó��Mô ý ô Ê +RQpõ$�1�����ô ö�ôS��û�ô5ó"ôøù�ôúý��)�|õ:ù�üMõ0�Mó"ô�õ'��õ87��Oü�õôTNBý�ù õ��"�2üMõ���3�� ó�ôs®����>=�õ:ù�ó"ö�� ���"ý ô �Mô ó�� Êl¡ � ü�� �VU ú U ¯VW�W)X8ü � ��U ú U ¯ ° @ W�W � °�ü�� � @ +ÞYH6 ü �:ö1�2�ô<ý#�có��2ö¿ó"ôC��õ:ö��Z/Võ:ù���õ���üsô U ��õ:ù�ô5ö8ô ��õ87�õ:ó��2ö>W¿ü�õ�ù�ô5üMõ���3�� ü�� ô5õ:üõ��"ù��3NO� �|õ:ó�õ��� �1ô ó��sô ý ô Ê ôúö�üMõzó�ô5üIü � � õ:ù��þý#�E�»ó�ôúüIô5ù�ù��2ù{ô -�û ��3�� ó�ô5ü �û��Yô5ù��8ó�ô4��õ:ö��2ö+

5 �)�Yô ýÿõVù�� �:ö [¤ô û�ô�/���%)������Fô ü�õøö�ô����3�� ? + ?8@ %¸ôúö\�¿û"÷0-$�õ���sü]� �E��ù��P/9�Mö�õ:ù§õ���ù��PNO���Zõ���� � ô5öô����D�M ù�����õ:ö¡ó�ôúüR�2ù�ó�ô ô ôúüR�5õ:ö�� ó"ô!��õ:ö��^J$7��Zõ^��õ:ùÕý#�Mù¡ó�ô-ü�õ�=�� �_��:ý ôúö��Möhó�ô!�Sû�ô-ô5üôúù�ù��:ùøö�ôK��)�E�`�:ù�ýÿõ8õ$��ù��3NO� �|õ:ó�õ��Yô ý�ô(��)�E�Ea!b)c]+d�e�f

gKhjiVkRlnm9oqp�r1hjm9s)i"oqm9tvuvpLuGi"r^uGm9l&s)p�w_xy{z8| l{i~}L�? + ? % @ +���% @ +��O% @ +���%L��+ ? %���+ ? %���+���%��O+ ? %V�O+ @ %V�O+���%���+ @ %L��+���%V�O+���%V�O+��O%��O+��O%L��+ ? %L��+ @ %

��+���%L�O+���%���+��O%V��+���%L��+���% ?PA + @ % ?3A +��O% ?)? + ? % ?8@ + ? % ?8@ +���% ?8@ +���% ? ��+ ? % ? ��+ @ % ? ��+���% ? ��+��O+

� ��� ���Z�ú��� �¿�����6���ª ��� ���}¢z¨¬�¬ Âw¢O�嶤���QÛO® ¬ ³_¼_Âc��¦;���ò@ó�ô5õ:öø÷,ù�ôúö�û�üþýÿõ:ó��2ö����õ:ö�����2ö Þ�H NO�sö�ý ô ��ù��)�"üMô�|õ:öE�Sû�ôaö�� ôúö�ý õ���üMôúö ó�ôúö�ó�ôaôúü0��û ý��zó�ô�/9�MöÕýÿõ>ý�ô*��2ù�� ��U �3ô��cû"ô9� õ:ö1/Võ:ù���õ���� � ôúö¿ô üMõ:ö<�� ó�� ��� � ôúö1� � ��Mõ:üMôúö �Z�E�có���JL�5õ ô5üS��)�E�`�:ù��ý õ����sô ý#�>õ:ö�� ýV��:ý�� ���»ó�ô�ü�õ>ö��2üMû���P�� W��1ô5ù����Sû�ôjö�ô���)�E�"�2ù�ý õ ó"ô�-{�2ù��|õ��¿û"÷� ô5öÕýÿõ���üsô(�5û�õ ó��=ö�ôIüsô5öøõ��"ü � �5õ!��sô5ùÕý#�2ö_�2�ôúý��Bó��:ö û��2�ôúù�����2ö�+S 9� ü �2ö_�"ù��)��üsô�|õ:ö¡¢¤£ ¥ +

?8@O?

Page 130: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

5 �)�Yô ýÿõVù�� �:ö ¦'�:=�õ�÷�ó�ô�J � ��� � ôúö=ù�� � û�ù��2ö�õ:ö �¡ù�ôúö�û�üþýÿõ:ó��:ö���� �5ù�ôúý��2ö � ô ôúù õ:üsô5öYô ôúö�ý õö�ô����P�� %v�1ô5ù���ôúö§�����"�2ùÕýÿõ ý ô6ô ý ô ó�ô5ùK�1ô5ù�-�ô��úý õ��|ô ý ôYô5ü�ô;7�ô����"ü �C�Sû�ô|õ���õ:ù�ô�5ôô ü��2ö¡õ���û ý�ô5ö%1õ:ö�M ��)�E�8ü �:ö_�cû"ô-ö�ô4/9�sô5ù�� ô �úü�õ:ö�ô�+

¨&©ª¨ ଫB­¯®�°�®;«²±�³´³Gµ9¶�·¹¸�®�º�®;±�·6±»º�®�°(³G·¹º�¼Y½C¾$³Gµ9¶�·¹¸�®�º�®�±�·6±ò@ó�ô5õ:öø÷,ù�ôúö�û�üþýÿõ:ó��2ö����õ:ö�����2ö ¿YH ü'À�Á8 £�Ã�£ ÁÄÀ�ÅCÅ ¡¢ÇÆ�Èj£ É £ À Æ À É £ à ŠÆ$É ó�ô,û �2�ôúý#�có��jôúö=ô5üS��� 7�û ý�� ó"ô,ü �2ö

Ê�Ë bVÌG%ÍÌZÎqÏ4%�ýÿõ:üsô5ö��cû"ô6ü�õ=ö��:üMû����P�� Ð û��2�ôúù�����õ|ó"ô!ÑÓÒ Ë ÌVÑ"%LÑ U A W Ë ? %"�úû��E��üMôü�� �!Ô3Õ�ÖZÑjÔ Ë A �5û�õ ó��Yô5ü*�2�ôúý#�có��=ö�ôJõ��"ü � �5õ1�� ýÿõ$�ZõV� �6ó�ô5ü*��õVö��^b*+¿  Bô{ó����5ôC�Sû�ô{û �2�ô<ý#�có��aô5ö�×0Ø;Å ¡¢ÇÆ�ÈjÉ ÅYö���ö�û�ó��)�E� ���jô5öÕýÿõ����sü �só�õ:óèü�� ô5õ:ü� �5üsû"÷2ôFô5üEö�ô�������ü�õ �4� ��Sû��sô5ù�ó��-ó"ô(Ï4+6[¤ô����có��K�cû"ôHö��Eû �2�ô<ý#�có��Jô5öS×��@ôúö�ýÿõ$��üMôô ý�� �úô5ö�üMõhö��:üMû����P�� § û��2�ôúù�� �5õhó�ôBÑ Ò Ë ÌVÑ4�� <Ù ô'ÌÄÚ A õ���ù��3N����ZõhõhüMõhö��:üMû����P�� ý�ô*��2ù�� ��õ8ô ÜÛ ôúüD� J �sý��)Ý�+ H ö¡ó�ô���Mù�%�ü ���!Þ�Õ�ßLÖ�Ñ U{à W Ë ü � �2ÑjÔ Ë A +5 �)�Yô ýÿõVù�� �:ö á û �Sû�ôIô ü�õ6ö�� � û��Mô ý�ô¤ö�ô����3�� ö�ô(/:ô5ùL�õ8û ���ôúý��Bó�� � ô ôúù õ:ü`��õ:ù�õ¿ó�ô���Mó��sù ü�õ

×��@ô5öÕýÿõ����Mü �só�õ:ó ó�ôZü��2ö!���ôúý��Bó��2ö-ó"ô Ù û �� ô��ªâOû"ý�ý õN÷ã=�õ:üMüMõ:ùIô5üUó��)�E� ����ó"ô ô5öÕýÿõj����sü �só�õ:óNü � ô�õ:ü¤%"=�õ�÷Ä�Sû�ô8ö õ$�3ôúù¤ü�õ:öhó�ô�J � ��� � ôúö0�2ù�� � � õ:üsô5öFó�ô¿ô5öÕý#�2ö0�� �úô�"ý��2ö¤÷õ��"ü � �5õ:ù�üMõ:ö�ô �5õ:ö��:ö���� �úù�ôúý��2ö+

¨&©Çä å�µÓ¶�·¹¸�®�º�®�±�·6±æ±�³ç­ è³D¶�«�±�«éµ~±�³´êìë�°(íé³Í¾$î´ë'¶O¶�·ò@ó�ô5õ:öø÷,ù�ôúö�û�üþýÿõ:ó��2ö����õ:ö�����2ö ¿ïH6 ü �2öE�2�ôúý#�có��2öYó�ô Ù û �� ô��ªâOû"ý�ý õ>ô5üFó��)�E� � �dó�ôNô5ö�ý õ����sü �Mó�õ:ó�ü�� ô5õ:üøö�ôôúö��5ù�� �1ôÄ���)�E�ñð Ê ÎòÏ ó ô U¤Ê WPó�Ú ?�õ ó�� ó�ô�ôÉô5ö���Môúù�ý õ:-�û ���P�� ù õ���� � õ:üüsü�õ��|õ:ó�õKö;÷ Ã`ø>£�ùÁ à À�Å Æ Â!ú É £ û"ø�ÆÓø#£�ùÁ à +¿ü, õ!-�û ��P�� ó�ôIõ��E��ü �.JL��õ����P�� ù�ôúö��"� ó�ôIõ8ü�õK-$��2ù��¿û"ü�õ!ô UnÊ W Ë ?¹ý Ê9þÿ�� U�� X

× Ê W���� þ? ó�� ó�ô þ? ô5ö�ôúü�/2ô��úý��2ù6�5û"÷2õ:ö¹��9�2ù�ó"ô õ:ó�õ:ö�ö�� ý��Bó�õ:ö ? +\[¤ô¡õ��Sû*�M ö�ô_��û�ô5ó"ôó�ôúó�û����Mù!�Sû�ô,ôúü � ù õ:ó��ðó�ô5ü û��|ôúù õ:ó��:ù-÷ ó�ô5üQó�ô �)��� õ:ó��:ù-ó�ô�ô ô5ö�ýL�õaõ���Výÿõ:ó���"�2ùøô5ü �û��|ôúù��8ó�ôIôúý õ���õ:ö�+

¿ò, �2ö_�2�ôúý#�có��2öøó"ô Ù û �� ô��;âOû"ý�ýÿõ8ô�NO��ü �M ���sý#�:ö �=ö�� ×��±ô5ö�ý õ���üsô5ö+¿ , õ -�û ��3�� ó"ôZõ��E��ü���JL�5õ���3�� ó�ôYû ���ôúý��Bó���ó�ô Ù û �� ôT�;âOû"ý�ýÿõ{ó�ô��:ù�ó�ô

U ó�ô§��� ö��Mö�ý�ô ����õ]W�Ð/2ô5ù���JL�5õ�ô U¤Ê W Ë ?Sý Ê� ? �jý Ê��� @��jý������Pý Ê c � �jý�� U¤Ê c ß � W�+ O�Uô5üB�2�ô<ý#�có��ðôúö¿ô�NO��ü �M ���sý#��ó�ô��zô<ýÿõ���õ:ö¿ü�õÐ� � û�õ:üMó�õVó>ö�ôC�5û��E��üMôYö�� ô5üUýO�ôúù��E� �� U¤Ê c ß � WT+

?8@)@

Page 131: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

¿�� õVù õ,ó�ô���Mó��sùOü�õ�×��@ô5öÕýÿõ����Mü �só�õ:óaó�ô=û �2�ôúý#�có��,ó�ô Ù û �� ôT�;âOû"ý�ýÿõ �Ð=�õ��5ô-Kõ:üþýÿõ^��� �9�5ôúùJôúü�õ:ö��3ô��úý#�Nó�ôúü�ó��)�E� ���Zó�ô=ô5öÕýÿõ����Mü �só�õ:ójü�� ô5õ:ü %`��õ:öÕýÿõC��)�E��ù��)��õ:ù�Sû�ô,üMõÄ-�û ���P�� ó�ô õ����"ü ��J���õ����P�� ý#�Mô ôZý��Bó��:ö6ö�û"öE�"�2ü��2ö%�ö�� ü �:ö!=Sû����sô5ù õO%Uô ô5üö�ô�E� ��üMõ �8ó�ôúù�ô�>=���%�÷ ý#�sô ô��~��2ó�û�ü��=õ���Výÿõ:ó����"�2ù ? ô ô5ü ôª7�ô§���Zõ � � õ:ù�� ��+

5 �)�Yô ýÿõVù�� �:ö ¦'�-ô5ö ô�5ôúö õ:ù�� �§�|ô����2ù�� �5õ:ùÀü�õ�-$��2ù��¿û"ü�õIó�ôHüMõ4-�û ��P�� ó�ôHõ����"ü ��J���õ����P�� �1ô5ù��ö�M ö õ��1ô5ùOûBý#�Mü�� �5õ:ù�üMõE��õVù õ ó�ô���Mó��Mù¤üMõ�×��@ôúö�ý õ����Mü��Mó�õVóD+4Qpõ��!�����ô =�õ�÷��Sû�ô=ô ý ô ó�ôúù��� �5üMõ:ù��só�õ:óÄ�`�2ù��SûB�ô¿ôúüpó��)�E� � �=ó�ô¿ôúö�ýÿõ$���Mü��Mó�õ:óNü � ô�õVü¾ö�ô¿ô5ö��5ù�� �1ô6ô ýO�ô5ù���� �2öó�ôIôúüMü�õ6÷ ö�û�ö���ù��)���Môúó�õ:ó�ôúöFõ:ö�� ýL��:ý#����õ:ö�+d�e�f

gKhjiVkRlnm9oqp�r1hjm9s)i"oqm9tvuvpLuGi"r^uGm9l&s)p�w_xy{z8| l{i��D�? + ? % ? +���% @ + ? % @ + @ % @ +���%L��+ ? %V��+��O%L��+���%L��+���%L�O+ ?)? %L��+ ?8@ +

� � ��� � "!$#'��%�&(')!Z�+*,%-&ä_©/. 0�·216è«43V­üë�º�· ±�³65G®�°"5*«87�ë�°S¶�«éµò@ó�ô5õ:öø÷,ù�ôúö�û�üþýÿõ:ó��2ö����õ:ö�����2ö

¿ H ü4�2�ô<ý#�có��ió�ôdó���-�ôúù�ô ���õVö J �sý õ:ö �� ö��MöÕý ôdô5ö�ô ����õ:ü��|ô ý�ô>ô ö�û�ö�ý��sý�û��Mùó�ôúù��./:õVó�õ:ö<��õ:ù���Mõ:üMôúö1�`�:ù<��9��Mô ý ô5ö�� �5ù�ô�Yô ýÿõ:üsô5ö8ô�/:õVüMû�õ:ó��2ö8ô ��sô5ùÕý#�2ö �có��2ö�Sû�ô4�� ö�ý��sý ûB÷2ô û õ=ó��Mö��5ù�ôúý#����õ����P�� ó"ô5ü§ó��)�E� ���!��� ö��só�ô5ù�õ:ó���+

¿  O�øö�ô,ó��Mö��5ù�ôúý#����õaü�õ à �� ��õVö��aýÿõ��|õV� ��bi÷èü�õ�Ñã�� ��õ:ö��dó�ô,ýÿõ��|õ"� �9 %��� ö��só�ô5ù��õ ó��2ö�ôaü�õ»ù�ô5ó û �.-{�2ù��Yô U à�:<; Ñ�=�W Ë U�> ý@? b ; ÿ ýBA 9 WT%hô ý�� �úô5ö{ô5üüMõ���ü�õ$���õ �DCFE U à�:<; Ñ�=�WÀö�ô'��û�ô5ó"ôOõ���ù��PNO���Zõ:ùé�"�2ùQôúü3üMõ���üMõ���Mõ �Ió��Mö��5ù�ôúý#�6ó�õ:ó��1�"�2ùüMõ!-$��2ù��¿û"ü�õ¿ó�ô4�� �����û ý��2öCHGJI�E U{à�:K; ÑL=�W Ë E U{à�: ß � ; ÑL=�W\X @ E U{à�:K; ÑL=TW ý E U{à�: ��� ; Ñ�=TWb �

ý E U{à�:K; ÑL=�ß � W\X @ E U{à�:K; ÑL=TW ý E U{à�:<; ÑL= ��� W9 � M[¤ô�=�ô��>=��Zö�ôOý#�Mô ôDCHE U à�:<; Ñ�=�W Ë CHG�I+E U{à�:<; ÑL=TW ýN� U b � ý 9 � WT+

¿ H ü�ü�õ��"ü�õ�����õ �=ó��sö��úù�ôúý���% õ$��ü ����õ:ó��|õZû õ�-�û ���P�� ó��Mö��úù�ô<ýÿõZó�ô�J �só�õZô ü �2ö �có��2ö�%PO : =j%¹���)����õ:ù�ý�ô^�� ôúü�üMõ���ü�õ$���õ ����� ý#� û��aü��2ö1��ù�� ��� �����2öJó�ô5ü&�~�õjNO� �E�

?8@ �

Page 132: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

��õVù õ^-�û ��� � ô5öOö�û���õ:ù��~�� ����õ:ö U CHERQ A Wh÷jó�ôúü��Ä�M� � �E�E��õ:ù õ^-�û ���� ô5öOö�û��1ô5ù��õ:ù��Ü�� � �5õ:ö U CHETS A W�+¿ , õ�ô�5û�õ���3�� ó�ô � �)�Mö�ö�� XUCHE Ë(V %EXWWZY�[ Ë]\ %�ô û ù�ô��úýV�õ �� û�ü���ô Ë^ >�;�_J`�a ^ ÿ ;�b ` ó�õ6üsû � õ:ù�%Bõ$��ü ����õ ó��6ô5ü"�2�ôúý#�có��-ó�ôHó��.-�ô5ù�ô ����õ:öéJ �sý õ:ö%Bõ:ü"��ù�����üMô��Zõ

XcCHG�IdO : = ËeVd: =8%fO : = WW Y�[ Ë�\g: =P+ � �2ùFô5ü*��ù�� ��� �����Yó"ô5ü*�~�õjNO� �E� U ÷{ó�ôúüv�Ä�M � �E�ÓW�%cô5üö��Mö�ý�ô�|õ8ü � ô�õ:ü3ù�ô5ö�û�üsý õ ý ôIô5ö����)����õVý#����üMô¤ó"ôúý ôúù��E� õVó���pý��Mô ôJö��2üMû���P�� �û � �5õ�+¿²� ý#�Mü�� �5õ ó����cû"ôYôúü�ü�õ$��ü�õ�����õ �Zó��sö��5ù�ôúý���õ$��ù��3NO� �|õ,õ:ü�üMõ���ü�õ$���õ �^��� ý#� û��

=�õVö�ýÿõ4�2ù�ó�ô @ %Sö�ô���û�ô5ó"ô'��ù��)��õ:ù¹�Sû�ôFü�õIõ���ù��3N����Zõ$��P�� �"�2ù�ó��.-�ô5ù�ô ����õ:ö6J �þýÿõ:öÀó�ôüMõ¡ö��2üMû���P�� ó�ôUü�õ¡ô�úû�õ����P�� ó�ô � �)�Mö�ö�� ô û ù�ô��úýL�õ �� û�ü��'��� /2ôúù � ô�õhü�õ&/:ô5ù�ó�õ:ó�ô5ù�õö��2üMû����P�� �5û�õ ó��8ü�õJó��Mö��5ù�ôúý#����õ����P�� ö�ô0/Võ!=�õ���sô ó��!�Ü�õ:öéJ õ�+ 5 � �5ù�ôúý õ��|ô ý ôOö�ô�úû����"üMô��|õjN!ó E U{à�:<; ÑL=TW�X�O : =]ó Ë � U b � ý 9 � W�+5 �)�Yô ýÿõVù�� �:ö H ö0-�û ó�õ��|ô ýÿõ:ü¾ô ý ô ó�ôúù¤ü�õYö�ô ��Müsü�õ��Mó�ô5õ|ô ü�õE�cû"ô¿ö�ô§��õ:ö õ|ô5üv�2�ô<ý#�có��Zó�ôó��.-�ô5ù�ô ����õ:ö_J �þýÿõ:öø÷{ö�ô5ù���õ���õ$�-ó�ô-õ���ü�� �5õ:ù�üMõ!� �úüMû�ö��Zõ=ô�úû�õ���� � ôúöHó��.-�ô5ù�ô ý ôúöhó�ôüMõ|ó�ô � �)�Mö�ö�� + , õ�-$��2ù��6û�ü�õYó�ô1�� ��^��û ý#�2öHô5öOû ö�� �E��üMôK��õVö��C��õ:ùÕý#���5û�üMõ:ù'�Sû�ôý��Bó��:ö6ü �:ö6õ:üsû�� �2öIó�ô�1ô5ù�M õ ö�ô5ù!��õ���õ$�5ô5ö6ó�ôZó�ôúó�û����Mù U �� ýO�ô5ù���� ��ó"ô ô5ù�ù��2ù#W�+

H üv��ù�� ������ �Yó�ô5üR�Ü�õ8N������ U ÷Nó�ôúü\�Ä�M �����]WQó��Mö��5ù�ôúý#�{õVö3�M ��)�E�ZüMõ|û ����só�õ:óðó"ô¿ü�õö��2üMû����P�� ó�ôúüBôúö��Sû�ô�|õHó�ôQó���-�ôúù�ô ��Mõ:övJ �sý õ:öR��õ:ù õFü�õhô��5û�õ$��P�� ó�ô � �)�sö�ö�� ö�� ö�ûO�JL���Mô ý�ô�Yô ý ô¤õ:ö�ô��cû�� ��üsô5ö&��õVù õ-ö�ô5ù&�5õ���õ��Hó�ôHù�ô��ù��Bó�û���Mù�ü �2öQö�� õ�÷cû�ó�õ8õ:ó������� õ:ü¤+, õ§�"ù�û�ô���õ¿ó�ôHüMõ§��� /2ô5ù � ô ���õ¿ó"ôHü�õJö��2üsû���3�� ^ û����ô5ù�� �5õ6õ6üMõIý�ô*��2ù�� ��õJô5ö û �`�9���~�õ:ö����)���"üMô;7�õF÷ �Iö�ôøù�ô�Sû��sô5ù�ô��~�õ:ö��Sû�ô��� �O�úô5ù�üMõHô�NO�MöÕý ô ��MõIó"ôøô5ö�ô¡ù�ô5ö�û"üsýÿõVó���+

d�e�f

gKhjiVkRlnm9oqp�r1hjm9s)i"oqm9tvuvpLuGi"r^uGm9l&s)p�w_xy{z8| l{i�hD�? + ? % ? + @ % ? +���% ? +��O% ? +��9% ? + ?PA % ? + ?8@ +

i j �� �� k!l*mn&�')!Z�+*,mo&H ö�ý�ôZ��õ��D�M ý û"ü �»ôúö ô5üã�û � ���èô ôúü0�úû�õ:ü¤ü��ã/9�MöÕý#�zô üMõ:ö^�úü�õ:ö�ô5ö ó"ôjý ô�:ù3�M õ �zö�ôõ87�û"ö�ýÿõ^J�ô5ü �Yô ý�ô8õZü �^�cû"ô=õ���õ:ù�ô�5ô6ô ü�õ:ö �:ý õ:ö(� �E��ù�ô5ö õVöHó�ôúü\�5û"ù�ö���%*=�õ����sô ó��õ:ü � û �:öC��õ��1��� �2ö{ó�ô��2ù�ó�ô ÷ ù�ô5ó"û����� � ôúöðõVü����M� � �E�èó�ô>õ:ü � û õ:ö,ö�ô���� � ô5ö+H ö�ô ��Mõ:ü �Yô ý�ôOô üMõ:ö&�úü�õ:ö�ôJó"ôIý�ô�2ù�M õ¿ö�ôJý�ù õVý õ:ù�� �úû�õVý ù��8ý ô�|õ:ö�

��+ ? �Uò ý ù��Bó�û����3�� õ:üD�2�ôúý#�có��8ó�ôJô5üsô�Yô ý#�:ö&J �sý��2ö+��+ @ �4pL�2ù��6û�ü�õ����P�� õ���ö�ý�ù õ��<ýÿõ8óB�ô����Mü ÷�/Võ:ù���õ���� � õ:ü +��+��j� � ù�� � ù õ��|õ���3�� ÷,ôúö���õ$�� �:öFó"ôJôúüMô��|ô ý��2ö_J �þý#�2öøô ó��:ö�/Võ:ù���õ��"üMô5ö�+

?8@ �

Page 133: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

��+��$�4q�ù�ô�/2ôK� ý�ù��có�û�����P�� õ=ü�õ1��� /2ôúù � ô ��Mõ�+H6 ö�ô � û��só�õZö�ô!��õ:ö�õ:ùL�õZõ|ù�ôúö�û��E�Mù�ü �2ö¡÷Ð�Sû�ô5ó�õVùL�õ �úü�õ:ù��2öhü��2ö��� ý ô �Mó��2öHó�ô!��õ:ó�õû �>ó�ô�ô5üsü �2ö�+~¦��ã�)�"ö�ýÿõ ý�ô�%_��õVù õdô�/9�sý õ:ù��� -�û"ö�� � ô5ö�% ö�ôÐ� ó�� ��õ õ��Sû*�M ü�õZ���2ù��ù�ô5ö��"� ó"ô ����õ»ó�ôðô5ö�ý õ û�ô�/Võèó��./9�Mö��3�� ô ö�ô���� � ô5öC�� ù�ôúö��1ô�úý��iõ>üMõ>ó�ô�ü �2öõ��"û ý ô5ö�

, õ û�ô�/Võ|ö�ô�����P�� ��+ ? ��:ù�ù�ôúö��"� ó�ô-ô5ö�ô ����õ:ü��|ô ý�ôJõYüMõYõ ý�� � û�õE�1ô5ù��|ôTNBý�ô �ó��só�õ��� ôª7�ô�E��ü �2öHù�ô5ö�û�ô5üþý#�2öIó�ô<ýÿõ:üsü�õ:ó�õ��|ô ý ô6ô ó�� �Yô ö��P�� û � U �Sû�ô=ô üMõ���õ ��� üMõ<��õ:ù�ý�ô§� ý ù��có�û��<ý#�2ù���õ¿ó�ôK��+��O+ ? W�+ , õYö�ô����P�� ��+ @ õ���õ:ù��5õYüMõ:öøö�ô������ ôúö0��+ @ %��+���%6��+��a÷���+��ðó�ô,ü��2ö8õ���û ý�ô5ö��1ô5ù��jý�ô �sô ó�� ô �5û�ô ý õ:�Sû�ô,üMõ���õ:ùÕý ôZý�ô*��2ù�� ��õù�ô�-�ô5ù�ô ý ôHõJüMõ:ö�ó�ôúù���/Võ:ó�õ:öÀóS�ô���süMôúöÀ÷=ü��2öÀô5ö���õ�����2öÀó�ô0 O�)�"�2üMô�/<�Sû�ô5ó�õK��� � �E� �5õ:ó�õ�+¦���:ý ôúö�ô��cû"ôhô ü �:öÀõ���û ý ôúö�üMõIö�ô����P�� ��+����� ý#�sô ôhõIü�õ:ö�ö�ô���� � ô5öS��+��¤÷���+��§�Sû�ô �-ö�� �Ü�õ:öé�Sû�ô¤ôª7�ô�E��ü �2öé��õ:ùÕý#���5û�üMõ:ù�ôúö+ , õJö�ô����3�� ��+��!��:ù�ù�ôúö��"� ó�ôHõ6ü�õ4��+��-ô ôúüÍ��õVö��<���só�� �Yô ö�� � õ:ü�÷,õ6û õ��"û�ô õ1��õ:ù�ý�ô¤ó�ôOü�õ§��+��9+ @ +p\� õVü �Yô ý ôFü�õ6ö�ô����P�� ��+��ZôúöHû õ���ù�ô�/2ô!�|ô ��3�� ó"ô6ü �:öFù�ô5ö�û�üsý õ:ó��|ý�ô*��2ù�� ���2öhó"ô!��+��Y÷{ó�ô-ü�õ���õ:ùÕý ô4J õ:üó�ô4��+��O+ ? ÷C��+��O+ @ +

r ©/. sÓ°S¶t3L«�±4ë"5u5G®*è«S° ·¹ºE­ è³*¶�«�±�«²±�³´³vº�³v­ ³v°&¶�«éµ F °�®ª¶�«Bµvxwty�z�{}|�~�y+{�û�üþý�z�w�� {����z�{����� {

¿ìH ü9�2�yúý#��w��cwty�y5ü�y�ny ý#��{RJ �þý#� {,z���ü�� �Lz�w��Uzhû �t~��)��ü�y���z�wtyS��� ý#� ~ �Hý�~�zj�ý�z�w�y�z��t~��3NO� �oz�~�ü�z"{��2üsû���3�� wty ý�~��Dwty¡û y�{���z����� U wty_-�û ��� � y�{>W,w�y�w�� �ny {��P�� J �sý�zO%ty�{/y ����z:ü��oy ý�y�z=ý�~�z3/¹�y�{�wtyúüuy�{��Sûty���zn{�� � û���y ý�y��6 �ycy+{���� � yUyúü�y�{��tz�����H� ËB�4U�� � ;J� � ; MLM�M ;J��� W�wt� wty ��: {�� -�� ����� y+{ U ö;÷ à Ø

ø#£ Á à Š¡&È�Æ$¡ ÅTW�{�y �������z�{ U�� �M ��� ��z��ny �� y�� � yLz���y�{�z � ~������ {#W�z�{/�O����z�wtz�{,z�� z���z�~ � � ���P�� wty+�uwt�)�E� ����+�' �y�{������ y��n�)�oy �� �z y�z��ny �� y§����ynEqÎ���%fy�{���~�� ����y wt��E Ë2��������� % |¡{��¢ ^ E `�Ë A y�{Hy+�&�t~/�)�t��y���zÄ����y�{�yC�£����y+~�yl~/y�{/� ��/�y�~%�{/yC� �E�¤� y���z ø Á à À £nø>£�ùÁ à À�Å¥ Æ$É Å�¦�§ £ à ¨ ¢ ^ E `�;J� I�© Ë A 9 Ë ? ; @ ; MLMLM ;Jª« £� y � ~�z wt����� ~_��z�~ � y+{%�y�/ « � z w���z�{�¬M �t~/� ­t��y���z�{}wty�~�y � �t��z�~ « w�z�wD+�0 �yHy+{�®�~ « ­�y ��z�{U®�� w « ® « � y+{k~�y�{/�t� � z �� y+{D®+�)�n��� { « { � y�ozl� « yLz��\× þ�qË þÿ

U × Ë �oz � ~ « �¯wtyH~ « � « w�y��% þÿ Ë / y+® � ��~Dw�yH®Lz�~ � z]W�+ �' z�/�y�F~�y+{��ty+� � ��%u��zl{������t® « ¬� z���~��3N « �oz�w�z-{�y+~�¬z �����°��� +¿�H6 y��u®Lz�{��Fwty4�t~���­t��y���z�{Pwty�®�� �� ��~ �ny � « �� y+~�/�z�����%���z-y���y+®�®+® « ¬� Ð z � ��t~�z��fy+{�{/�t­�w « / « w « ~�y+� « �� y+~�/�z����Hy ��z�~ � y�{ « � ��z���y+{P|�®+� { « wty�~�z�~c� � y y�~�z�wt����� ~

ö;÷ Ã"ø>£ Á à Š¡�¢ Å � Æ À�Á'�£�ty�/�z���y ? y ® « y�~ � � ��w���| A y ��� {�wty�N¬z�{�%�®+� y��V�t~/��wt��® � �y+{�®Lz���z�~ Û ��{���z���Ý ¨ V�;�\ © ˲±�V�\ +

?8@ �

Page 134: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

¿I�' ®Lz$�-­ « �ky y+� ¬���oy+~��kwty���z�~ � y+{%�|<��� ~ � z �� ��y ��z�{�-�� ® « � y+{X®+� { « wO�y+~�z�w�z�{%�{/y � ~�z�wt�t®+y"y �t~/� ­t��y�oz�{4{/y ® « ����� { U � « yLz���y�{#Wy � ®�z��-­ « ��wty0/�z�~ « z�­���yy ��z�{ « �� y � ~�z���y�{_�£�ty�wty�J y ����{}y���y��oy �� � {�wty���z1�oz � ~ « �Uwty�~ « � « wty���+5 �)�ny �� z�~ « ��{ ³ �y¹=�z�­�~�¬z z��t~/y w « wt����� {u®+� �� y « wt��{´wty�y+{ � z�{�y+®�® « ¬� { « {/y4y+{�®�z���z���wtyXz���� « ®�z�~y+�(�µ¬y � ��wt�Rwty$y+��y�ny �� � {�J « � � {¶z��t~/� ­t��y�oz�{lwty$®+� �� � ~ �µ� « yLz���y�{l{/y ® « ����� {

U w « � z$�o� {}w�y�� � « �¤� X�EVÒ Ò ý�· E Ë@V %�E U�> W Ë E U ÿ W Ë A WJ¸�{�z�­ « y wt� « ®+~�y��oy £� z�~�y�� ¬���ny�~/��wty�-�� ® « � y�{X­�z�{/yc{ « E y�®+y�{ « w�z�wowty�~�y��y � « ~�����{X®f¬z���®+�t����{6��z�~�z4=�z�����z�~,��� {y+��y�ny �� � {}wty���z<�oz � ~ « �"wty�~ « � « wty�$+

r ©ª¨ ¹(«X3V­�ë�º;·�5G®Gè«B° ·¹¸(µ9¶�3L·�5Ͷ�·¯±2è³v¸�®�ºE¼»º6·�3V®;·�5G®�«B°(·¹ºvxwty�z�{}|�~�y+{��t� � z�w�� {�­�¬z�{ « ®�� { ³

¿ , � {<�t~/� ­t��y�oz�{Hz$��� {<�£�ty¶{/yTz$�t� « ®Lz¡y+�&�µ¬y � ��wt�$wty¶y���y�ny �� ��{1J « � � {H{�y�t��y�wty y�{/®�~ « ­ « ~}y ��z1ö Ád¦�ÂC÷ É Æ]ø>£�ùÁ à À ùÅ Èj£ É>"U E ;�¼ W Ë ¢ U�¼ W ½ ¼ Î)�

wt� wty > y+{U� zE-�� ~��ozn­ « � « yLz�� U |¾{ « �µ¬y � ~ « ®Lz�%�®+� �� « �tzo|¾®���y�~�® « /�z]W�|T¢¿y+{U� z-�� ~���zT� « yLz�� U |À®�� �� « ��z]W�¸Pz��-­�z�{-wty�J « w�z�{Hy y���y+{���z�® « �Áwty¶Â « ��­¤y+~ � � �£�ty®+� �� « y yDzH��zH{�� ���t® « ¬� EG+¿ �� z0/ y�������y}{�y}y�NO�t~/y�{�zD� �t~/� ­t��y�ozcy {/��-���~��-�t��z�® « ¬� w4¬y�­ « � %�y+���µ¬y � ��wt�wtyTy���y�ny �� � {�J « � � {n{�yT~�y+wt�t®�y¡zÃ~/y�{�����/ y+~^× þ�çË þÿ wt� wty > I �4ËÄ>"UK� I ;J��� W-|ÿ I Ë ¢ UK� IPWT+ , zH{/� ���t® « ¬� z���~��3N « �oz�w�z-y�{ �Å������� +¿´, zK-�� ~��-����z�® « ¬� w4¬y�­ « ��y�£� « /�z���y"z���z§ö Ád¦�ÂC÷ É ÆÓø>£�ùÁ áÆ�Æ ¦ £ ÆÓø#£ Á ÃLÆ$É |�yTNO�t~�y+{�zH��z{/� ���t® « ¬� EH®����o��y��9�T¬M� « �n�}wty4� -�� ® « � z�� %d®�� ®�~/y � z$�oy £� y�wty �� >`U E ; E`WjX¯¢ U E`W�+¿ï, � {oy+{���z�® « ��{�wtyT « ��­�y�~ � ®+� ��� {�����y¡{�y � ~�z�­�z87�zÁy ��z�{<-�� ~����t��z�® « � y�{w4¬y+­ « �¤|�/�z�~ « z�® « � z��¤{�� y�{���z�® « � {�wty§ �� ­�� ��y�/"+¿ , ��{!�t~/� ­t��y���z�{¯wty+� � « ���qXcCHE ý�· E Ë(V y � z¡�Ä/�z�~ « z�{Dw « �ny { « � y�{z�w�� « � y -�� ~����t��z�® « � y�{�w4¬y�­ « ��y+{�®+��z wt�${/y « �E��� y ®�� w « ® « � y+{�wty�[ « ~ « ®>=t��y �=t���o� � ¬y y�z�{ U E6ó YJÇ Ë A WP�FwtyK¦cy+���oz � qU Y�ÈY Ô WWÉY�Ç Ë A WT+5 �)�ny �� z�~ « ��{ ³[kz�wt��� �t~/� ­t��y���z}{/��J�® « y �� y��oy �� yX{�y ® « ����� U y�{���y�® « z����oy �� y�XUCHE ý¯· E ËeV W

=�zL|<�£�ty�{�z�­¤y+~XyTNO�t~�y+{�z�~/����y {/��-�� ~��-�t��z�® « ¬� w4¬y+­ « �¤+ , z(-�� ~��-����z�® « ¬� /�z�~ « z�® « � z��y y�{ � y$®���~�{����£�ty+w�z�~�y+��y � z�w�zÃzÀ� {/y � � wt���t��z ��%_��y�~�� ��®���y�{ � zRz���y z�{y+{�-��ty+~����Êz�w « ® « � z��y��Xz���~�y wty�~/��z�+ 5 �)�o�¶|�z¾{�yE=�zÄ�ny ® « � z�wt��%Ë{/y�� « « � « �Lz�%

?8@ �

Page 135: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

�t~t¬z�® � « ®�z��oy �� y�{/yly�� « � « zO%���z���z�~ � y�����yl{�y�~/y�J�y+~�y�z¡��z � y�� ~�¬M zTw�yly�{���z�® « � {-wty ���­¤� ��y�/ U �£�ty �0��y�~ � y y+®�yPzcy�{ � zcz�{ « �) z � �t~�z]WT+ H {/y ® « z����oy �� yX���Á¬� « ®+������yS=�zL|�£�ty � y y�~�y �ny �� yDy�{��£�tyDy��uy�{���z�® « �nwtyD « ��­¤y+~ �_ z � �t~�z��uy y��G�£�ty�{�y � ~�z�­�z87�zy+{�Ì � ����y � « y y_��� ~ � ~���znÍJE�Í �Î�Ï�Ë ± E � ý U E Ò W � wt��Ðtwty�E Ò y�{���z§À�Å�¦ £<Æ�Æ À Æ À ùÅ È$£ É +H { � z�wty+~ « /�z�wtz¯y�N � « y�Ð�wty"zD��z§=tz�­ « � ��z��V��y�~�� « � « y+Ðtwt��wty�~ « /�z�~¹-��tÐt® « � Ðty+{P� « Ðty�z���y+{4z� ~��)�+� {%�®+�)�o�Hy+�D/�z���� ~�z�­t{�� ��� � ��+

r ©Çä Ñ)3L«BíX3L·¹­¯·�5G®*è«B° ¼ ³Gµt7(·�5G®;«Bµ²±�³æ³vº;³v­¯³v°S¶�«éµ F °�®ª¶�«éµ ³v°±�«éµ�º6·�3V®;·¹¸�º�³Gµ

vxwty�z�{}|�~�y+{��t� � z�w�� {�­�¬z�{ « ®�� { ³¿»� z�~�z¡z��t� « ®�z�~�y��XÒµ¬y � ��wt�Tw�yly���y�Òny�Ð � � {4J�Ð « � � { U � « Ðty�z���y+{>W"y�ÐÀ�tÐ�wt� Ò « Ð « �

U �¤� � «�Ó ��Ð�z�� WPw�y�Ô � {/y � ~ « z�Ð Ó �t��zF|¡{/yH®�� Ðt{ « wty+~�z�Ð$®+� Òn�^-��tÐt® « � Ðty+{"­�z�{/yH��z�{'ö;÷ à Øø#£ Á à Š¡ ú £ ¦ ùÆ Â £ À�Å}®+� ~�~/y�{/Õ¤� Ð�w « y+Ð � y�{+Ö

¿×� z�~�z¡®Lz�w�z � ~ « ¬z�Ð Ó �t���Ð=tz�|Ãz¾���¾Òجz�{ � ~/y�{K-��tÐt® « � Ðty+{¯­�z�{�y�®+��| ��{-{�� Õ�� ~ � y�{��� « Ðt®+����|�y�ÐfÖ H { � z�{_-��tÐt® « � Ðty+{�{/y�Õt�ty�w�y�СyTN�Õt~�y+{�z�~+Ù�®+� ж�tо®Lz�Ò-­ « �Hwty�/�z�~ « z�­t��y�{z�w�y�®��tz�wt�tÙ�y�Ð � ¬y�~/Ò « Ðt� {�wtyD® « y+~ � z�{�-���Ðt® « � Ðty�{cÕ « ~t¬z�Ò « wtyk®�z�Ð�¬� Ð « ®Lz�{�{�y+Ðt® « ����z�{�Ú � ÙÚ � Ù�Ú¯Û�Ö¿ Q´~�z�{Dy���{��t{/��w « ®�Üt�Ê®�z�Ò-­ « �¶wtyoÝ�z�~ « z�­t��yH��z¶®�� Ð � ~ « ­��t® « ¬� ÐÃw�yo��z¾Òoz � ~ «�Þ wty~ «�Ó « wty Þ wty�®�z�w�z¯~/y�® � ¬z�Ð Ó �t����{�y�y�N�Õt~/y�{�z�®�� Òn���tÐ�zD®�� Ò-­ « Ð�z�® « ¬� ÐH� « Ðty�z��twty�® « y�~ � z�{ Æ�¢ ¦ £nø Å ¡�È0ùÆ$¡�£nøTÆ$¡ ®���|�� {Py+��y�Òny�Ð � � {�{�� Ð � ��wt� {�����{�Õt~���wt�t® � � {Xy�{/®Lz���z�~�y+{Xw�yUÚ : Õ�� ~Úc=U�Fwty�{��t{�wty�~ « Ý�z�w�z�{}Õ�z�~�® « z���y�{+Ö¿òH �u®u¬z���®��t���Hwty��uÝ�y�® � � ~�wtyD®Lz�~ Ó zH����y�Ý�zHzFÕ�~�� ­t��y�Òoz�{}wty�®��tz�wt~�z � �t~�zny+ÐT�tÐtz|�w�� {�w « Òny�Ðt{ « � Ð�y�{�Öß � Òny�Ð � z�~ « ��{ ³à ­�Ý « z�Òny�Ð � y���z�Õt~�� Ó ~�z�Òoz�® « ¬� Ð � « y�Ð�y�Òجz�{ á���y�Ý�y�~Ë®���ÐD��z�{f®+��z�{/y�{ËÕt~�¬z�® � « ®Lz�{uá£�ty®+� ÐÁ��z�wty � y�� ~�¬M z�Ù { « ÐÁy+Ò-­�z�~ Ó ��y�{kÐty+®�y+{�z�~ « �¶{�z�­�y�~k��z�{ « wtyLz�{ká£�ty-â���Ðtw�z�Òny�Ð � z�Ð���Ãá£�ty¾{�yTÕt~�� Ó ~�z�Òoz�Ö H Ð�y�{ � y¡®�z�{��tÙ}{ « ÒnÕt��y+Òoy+Ð � y�Ü�zL|�á£�ty¡y+Ð � y�Ðtw�y�~�­ « y�Ð�y��{ «�Ó Ð « J�®Lz�wt�Hwty���� {}Õ��tÐ � � {cz�Ð � y+{�Òny�Ð�® « ��Ð�z�wt� {+Ö

r © r ã 3L³uºS³ç®�°&¶�3L«�±4ë"5u5G®Gè«B° · º;·ä5*«B°�ºS³Ë3Líé³v°"5G®�·vxwty�z�{}|�~�y+{��t� � z�w�� {�­�¬z�{ « ®�� { ³

¿æå ÐTy+�ËÒµ¬y � ��wt�Fwty�y���y+Òoy+Ð � � {_J�Ð « � � {�{/y « Ð � y�Ð � znz�Õt~/�3N « Ò�z�~��tÐ�zFâ��tÐt® « ¬� жEá£�tyoÕ¤y+~ � y+Ðty�®+ylz¾�tÐÀy+{�Õ�z�® « �¾wty�w « Òny�Ðt{ « ¬� Ð « ÐOJ�Ð « � z U y�ÐÀy���á£�tyo��z¶â���~�Ò-�t��z�® « ¬� Ðw4¬y+­ « � � « y�Ð�y¯{/y�Ð � « wt�ÓW}Õ¤� ~�� � ~�zná���y�Õ�y�~ � y�Ðty+®�y�zo�tÐTy�{�Õtz�® « ��wty¯w « Òny�Ðt{ « ¬� ÐCJ�Ð « � z

çdè �

Page 136: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

U y�� Ó y�Ðty+~�z�w��$Õ¤� ~¯��z�{�â��tÐt® « � Ð�y�{-­�z�{�yPWJÖ å �P��y�ÒozTwty ß ¬yLz$z�{/y Ó �t~�zÊá£�tyly��4y�~/~�� ~y+Ð�y�{ � zHz�Õt~/�PN « Ò�z�® « ¬� Ðny�{ � ¬zHz�®+� � z�wt�tÙ�{�z���Ý��-®���Ðt{ � z�Ð � y�{+Ù�Õ¤��~P��zDw « { � z�Ð�® « z¯wty"E¾z��y+{�Õ�z�® « �Fwty�w « Òoy+Ðt{ « ¬� ÐCJ�Ð « � z�Ö¿6� z�~�z « Ð � y+~/Ý�z�����{4y+ÐlÔ�|owt� Ò « Ð « � {XÕ¤� � «�Ó ��Ð�z���y+{�®�� Ð�Ý�y�N�� {�y�ÐlÔ � Ù � ��wtz¯â��tÐ�é® « ¬� ÐH®+� ÐF~�y Ó �t��z�~ « w�z�w-{���Jt® « y+Ð � y�{�y�z�Õt~/�3N « Ò�zc­ « y+ÐnÕ�� ~��� {�y�{/Õ�z�® « � {�wty�â���Ðt® « � Ðty�{� « Ðty�z���y+{ Û z � ~/� Þ ��{�Ý Ó y+Ðty�~�z�wt� {,Õ¤� ~���z�{�â��tÐ�® « ��Ðty�{ � yëê�z�wt�"�"Õ « ~�¬z�Ò « w�y�Ö å ÐHÕ�z�~ � « ®+��é��z�~uy��£Òµ¬y � ��wt��wtyPy+��y+Òoy+Ð � � {*J�Ð « � � {�®�� Ð�Ý�y�~ Ó y�~�¬zc®���z�Ð�wt�U{/y Ó z�~�z�Ð � « ®�y���z�®�� Ð�w « ® « ¬� Ðwty�~/y Ó �t��z�~ « w�z�w�~/y�á£�ty�~ « w�zFwty���z-{/� ����® « ¬��ÐfÖß � Òny�Ð � z�~ « ��{ ³å �¤~/y�{/�t� � z�wt�D~�yLz���Òny�Ð � y « ÒnÕ¤��~ � z�Ð � y�y�{Py+��{�y�Ð�® « �����D��y+Ò�zkwty ß ¬yLz�á£�tycÜ�zL|oá£�ty®+� Ðt��®�y�~�z��XÒoy+Ðt� {Dy�ÐR��z�â�� ~/Ò�z « Ðtw « ®Lz�w�zTy+Ð���z « wty�z¡z�Ð � y+~ « � ~�Ö Ù y�{�Õ�y�® � �Áz¾��� {~/y�{���� � z�wt� {�wtyDz�Õt~/�PN « Ò�z�® « ¬� Ð�Õ�� ~�â��tÐ�® « ��Ðty�{�� « ÐtyLz���y�{ U �tÖ è�ì Ù��tÖ è�ç Ù��tÖ è�è |C��Ö è �Hy+Ð��z�{}Ðt� � z�{>WPÐt�ny�{�Ðty+®�y+{�z�~ « �n®�� Ðt��®�y+~�Ð « Ð Ó �tÐt�tÖ

d�e�f

gKhjiVkRlnm9oqp�r1hjm9s)i"oqm9tvuvpLuGi"r^uGm9l&s)p�w_xy{z8| l{iÃíG�ç Ö ç Ù ç Ö è Ù ç Ö���Ù ç Ö���Ù ç Ö���Ù è Ö ç Ù è Ö è Ù è Ö���Ù è Ö��tÙL��Ö ç ÙV��Ö è Ù���Ö���ÙL��Ö���ÙL�tÖ ç Öî ï ð U*,m¶ñÊmn& ��L!Ê "%1�+ k&ï� òZ�+*6�LóÊ%�&,mô&©/. sÓ°S¶t3L«�±4ë"5u5G®*è«S°

vxwty�z�{}|�~�y+{��t� � z�w�� {�­�¬z�{ « ®�� { ³¿æõ � {_ ùÅ ¢ Á9À�Á ¡_É�£ à ŠÆ$É Å ¡ ÂC÷ É ¢¤£ ú Æ$¡ Á U À�Å 9 Ø ú Æ$¡ Á ¡ W�~�y�{/Õ¤��Ðtwty�СzH��z�â�¬� ~/Ò-�t��z

Iö =�÷tø · =TÑ$Ô3ß�= Ë bIö =�÷tø�ù = V,ú{à ÔPß�= ; ÑjÔPß�=�û M

å {¶wty�® « ~+ÙUÕ�z�~�zRÜ�z�����z�~^Ñgü�Ü�zL|ýá£�ty)®���Ðt��®+y�~���� { 9 Ý�z���� ~/y�{¶z�Ð � y+~ « � ~�y+{�³�Ñ�ü ��� ÙÑgü � � Ù°Ö�Ö+Ö�Ù�Ñ�ü � I Ö¿ á �tÐeÒR¬y � ��w��N®���Òo��y��¯z�Ð � y�~ « � ~¾{�yÀ��yÃz�{���® « z�в��� {�ú�Á É £�à Á8 £ Á ¡Ðø�Æ ¦ ÆÓø Ø¢ Å�¦ ùþ ¡3¢n£nø Á ¡

ÿ�únÊ û ËIö =�÷tø · = Ê

= | � únÊ û ËIö =�÷tø ù = Ê

=M

çdè �

Page 137: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

¿]õ zlwty���Ð « ® « ¬� Ð$w�y ø Á Ã�Æ Å�¦���Å Ã`ø>£ Æ |:Ád¦�À�Å Ã À�Å ø Á Ã�Æ Å�¦��OÅ Ã`ø#£ Æ y�{�{ « Ò « ��z�~�z���zwtyT��� {nÒµ¬y � ��wt� {nwtyT�tÐØÕ�z�{/��{�z���Ý �Àá���y$z�Üt� ~�zÃÐt�Ã{�¬� ���ÀÜ�zL|�á£�tyÊ{/�tÕ¤��Ðty�~lá£�tyÑ�ø-z�Õt~/��� « Ò�z¶z��Ý�z���� ~ « Ð « ® « z��\Ñ ú{à øJûJÙ,{ « Ðt�¾á£�ty^Ñ�=-z�Õt~/��� « Ò�z¾zÐÑ ú{à =�ûkÕ�z�~�z¾��� { 9Õt~ « Òny�~/� {PÝ�z�����~�y�{+Öß � Òny�Ð � z�~ « ��{ ³ÂUzL|)á£�tyn{�z�­�y�~D��z�â�� ~�Òoz Ó y�Ð�y�~�z��4wtyn����{DÒR¬y � ��w�� {�� « Ð�yLz���y�{kwty 9 éxÕ�z�{�� {�|Á��z{/y�Ðt® « ����zUwty���Ð « ® « ¬� Ð�wty}��� {,Õ¤� � « Ðt��Ò « � {Ë®Lz�~�z�® � y�~�¬� { � « ®���{�Ö�¦��kÜ�zL|Há£�ty}Ü�z�®+y�~�Ð « Ð Ó ¬�tÐy+{/â��ty+~ Þ �nz�w « ® « � Ð�z���Õ�z�~�z-z�Õt~/y�Ðtw�y�~}����~�y���z � « Ý �Hz-��z�®���УÝ�y�~ Ó y�Ðt® « zH�tÐ�z�Ý�y Þ á£�tyk{�y®+� Ðt��®�y�y�{ � y�®�� Ð�®�y�Õ � ��Õtz�~�zH����{}Òµ¬y � ��wt� {}wty��tоÕ�z�{/�tÖ

ô&©ª¨ q«S°(µ�®�µÓ¶�³v°"5G®;·vxwty�z�{}|�~�y+{��t� � z�w�� {�­�¬z�{ « ®�� { ³

¿ å �GÅ�¦�¦TÁd¦�À�Å ¢ ¦3÷ Ã`ø�ÆÓø#£�ùÁ à |�y+�vÁd¦TÀ�Å Ã À�Å ø Á Ã�¡�£ ¡3¢ Å Ã`ø#£ Æ {/ykwty�tÐty�ж®���Òo�-y+Ð�y��®�z�{��nwty���� {}ÒR¬y � ��w�� {}wty��tоÕ�z�{���Ö¿ å �f��~�wty+оw�yk®�� Ðt{ « { � y�Ð�® « zH{/ykÕt�ty�w�yDÜtz�����z�~4®+� ж��z-wty���Ð « ® « ¬��Ð��H®Lz���®��t��z�Ðtwt��tÐ��oá���y�Ý�y�~ « ��á£�ty ÿ�ú ç`ý Ê û�� � ú ç`ý Ê û���� Ó ú ç`ý Ê û Ë a Ê c ß � ýT� únÊ c ß � û®�� Ð�a��Ë ì

ú ®���z�Ð�wt� Ê�� ì û�Öß � Òny�Ð � z�~ « ��{ ³["y�У�ty�Ý ����z�{cw�y��Ð « ® « � Ðty�{c®�� ~/~�y+{�Õ�� Ðtw « y�Ð � y+{kÐt��~/y�á£� « y+~�y+Ð$�tÐÊy�{ â��ty�~ Þ �¶z�w « é® « � Ð�z��,Õ�� ~�á£�tyH|�z�{/� ÐÁ®�� Ðt��® « w�z�{kwty+�Õt~ « Òny�~"®�z�Õu¬��� �t����Ö å ��®�~ « � y�~ « �l® « � z�w���Õ�z�~�z®�z���®+�t��z�~�y��}� ~/wty�Ð�wty¶®�� Ð�{ « { � y+Ðt® « z)Ðt�Áy+{nÐ�y�®�y+{�z�~ « �)Òoy+Òo��~ «�Þ z�~����¡{ « y�ÒnÕt~/y¾á£�ty�tÐ���{�y�ÕtzTz�Õ�� « ®�z�~U��z�wty���Ð « ® « ¬� РÙf���l®+��z��y+{Dz�á£�u¬� Ò-�t®�Ü��¾ÒN¬z�{Uâ�¬z�® « �´á£�tyHÕ�z�~�zl��� {Òµ¬y � ��wt��{4wtyc�tÐlÕ�z�{��tÖ å � � y+� ~�y+Ò�z!��Ö���á���yUy�Ð���z�{XÐt� � z�{�z�Õtz�~�y+®�yUy+Ðly�{ � z�{/y�®+® « ¬��Ð{/yD{/�tÕt~ « Ònyky�жâ�z�Ý�� ~�wty�� � y�� ~/y�ÒozHÕt~ « Ðt® « Õ�z��fwty���z-{�y�®+® « ¬� ÐT{ «�Ó � « y�Ð � y�Ö

ô&©Çä �\¾$³vµÓ¶�·¹¸�®�º�®�±�·6±vxwty�z�{}|�~�y+{��t� � z�w�� {�­�¬z�{ « ®�� { ³

¿æõ zH®�� Ðt{ « { � y�Ð�® « zHwty�� ~/wty�ÐF�TÐt� « ÒnÕt� « ®Lz���z-®�� Ð�Ý y+~ Ó y+Ðt® « z�Ö¿  �y�w « ®+ycá£�ty��tÐoÒµ¬y � ��wt��y�{ ì Ø;Å ¡3¢ÇÆ�È$É ÅLÙ�y+{�y+Ðt® « z���Òny�Ð � y�Ù£{ « z���Õ�z�~ � « ~Xw�y�wtz � � {« Ðt® « z���y+{Õ�z�~/y�® « wt� {�{/yc� ­ � « y+Ðty�ÐF~/y�{���� � z�wt� {�Õ�z�~/y�® « wt� {+Ö å { � �Dy�{Xy�á£� « Ý�z���y+Ð � y�zDá£�ty��z�{}~�z�¬� ®�y+{}wty ÿ {�y�z�оwty�Òج� w��t���HÒny�Ðt��~}á���y¯�tÐ��o�F{ « ÒoÕ���y�{Pwty�Òج� w��t���H�tÐ��tÖ¿  �yn®��tÒnÕt��yHy�� ¢ Å�Ád¦�Å#Â Æ À�Å�Å���÷ £KÆ�ÆjÉ Å Ã"ø>£ Æ À�Å�� Æ$É ��÷ £ ¡3¢ ³ � z�~�zT��� {kÒµ¬y � ��wt� {� « Ðty�z���y+{�Ò��t� � « Õ�z�{/����zo®���УÝ�y�~ Ó y�Ðt® « zly+á�� « Ý�z���y�z���zn®�� Ð�{ « { � y+Ðt® « z�wty-� ~/wty�Ðo�ÃQ çê/�tÐ � �n®+� о��z ì éxy+{ � z�­ « � « w�z�wfÖ

çdè �

Page 138: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...

ß � Òny�Ð � z�~ « ��{ ³q�z�{ � zl®+� Ð$®�� Ð���®+y�~"y+� � y+� ~�y+Ò�z�w�y<[kz���á£� « { � |¡{�z�­¤y+~kz�Õt� « ®�z�~����oÕ�z�~�z�wty+® « w « ~��z-®�� Ð�Ý y+~ Ó y+Ðt® « zowty��tжҵ¬y � ��wt��Ö õ zHÕt~/�ty�­tzn{ « ÒnÕt��y+Òoy+Ð � yk{�y�y�{/­¤� Þ z�~t¬zny+о®+��z�{/y�Ö¦��Hy�{}Ðty+®�y�{�z�~ « �F®�� Ðt��®�y+~}��� {P~�y�{/�t� � z�wt� {}Õtz�~�® « z���y�{�Ù � y+� ~�y+Ò�z�{���Ö���ÙL��Ö���| ��Ö���Ùtá£�ty{/yDy+ÒoÕ���yLz�оy+ÐT��� {�z�Õt��Ð � y�{�Õ�z�~�zFw�y�Òn� { � ~�z�~/���tÖd�e�f

ç � ì

Page 139: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...
Page 140: C бвгезгй § ¡ ей Problemas resueltos DE GHP RTUHWHP YH ...