{"id":141227,"date":"2019-11-12T21:41:26","date_gmt":"2019-11-12T23:41:26","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=141227"},"modified":"2023-06-09T04:24:21","modified_gmt":"2023-06-09T07:24:21","slug":"problema-calcule-o-valor","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problema-calcule-o-valor\/","title":{"rendered":".Problema: Calcule o valor"},"content":{"rendered":"<p style=\"margin:10px\">\n<div class=\"g1n\" style=\"line-height:25px;\">\n<p class=\"tit\" style=\"line-height:20px;margin:10px\">Problema<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicado a partir do 9\u00ba ano do E. F.)<\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 1px; margin-bottom: 20px;border: 0 none\"\/>\n<p style=\"margin:10px\">\n<p><span style=\"font-size:13px;\">(<strong>OPRM<\/strong>, 2016- 3\u00aa Fase- Adaptado)<\/span>  Considere as equa\u00e7\u00f5es [tex]\\dfrac{a-b}{c-d}=2[\/tex] e [tex]\\dfrac{a-c}{b-d}=3[\/tex], com [tex]a,b,c[\/tex] e [tex]d[\/tex] distintos dois a dois.<br \/>\n<strong>Calcule o valor de [tex]\\dfrac{a-d}{b-c}.[\/tex]<\/strong><\/p>\n<p style=\"margin:10px\">\n<\/div>\n<p style=\"margin:40px\">\n<div class=\"g1n\" style=\"line-height:30px;\">\n<p class=\"tit\" style=\"line-height:30px;margin:10px\">Solu\u00e7\u00e3o<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 1px; margin-bottom: 20px;border: 0 none\"\/>\n<p style=\"margin:10px\">\n<p>Observe, inicialmente que:<\/p>\n<ul>\n<li>de [tex]\\dfrac{a-b}{c-d}=2[\/tex], segue que:<\/li>\n<p> [tex]\\qquad a-b=2c-2d[\/tex]<br \/>\n[tex]\\qquad a+2d=b+2c;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\textcolor{#800000}{(i)}[\/tex]<\/p>\n<li>de [tex]\\dfrac{a-c}{b-d}=3[\/tex], segue que:<\/li>\n<p>[tex]\\qquad a-c=3b-3d[\/tex]<br \/>\n[tex]\\qquad a+3d=3b+c.\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\textcolor{#800000}{(ii)}[\/tex]\n<\/ul>\n<p>Multiplicando a equa\u00e7\u00e3o [tex]\\textcolor{#800000}{(i)}[\/tex] por [tex]4[\/tex] e a equa\u00e7\u00e3o [tex]\\textcolor{#800000}{(ii)}[\/tex]  por [tex]3[\/tex] obtemos:<br \/>\n[tex]\\qquad 4a+8d=4b+8c\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\textcolor{#800000}{(iii)}[\/tex]<br \/>\ne<br \/>\n[tex]\\qquad 3a+9d=9b+3c.\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\textcolor{#800000}{(iv)}[\/tex]<\/p>\n<p>Agora, subtraindo [tex]\\textcolor{#800000}{(iv)}[\/tex] de [tex]\\textcolor{#800000}{(iii)}[\/tex] vem que<br \/>\n[tex] \\qquad a-d=-5b+5c[\/tex]<br \/>\n[tex]\\qquad a-d=-5(b-c).[\/tex]<br \/>\nLogo, [tex]\\fcolorbox{black}{#eee0e5}{$\\dfrac{a-d}{b-c}=-5$}.[\/tex]<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" style=\"line-height:20px;\">Solu\u00e7\u00e3o elaborada pelos <strong>Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n<p style=\"margin:10px\">\n","protected":false},"excerpt":{"rendered":"<p>Problema (Indicado a partir do 9\u00ba ano do E. F.) (OPRM, 2016- 3\u00aa Fase- Adaptado) Considere as equa\u00e7\u00f5es [tex]\\dfrac{a-b}{c-d}=2[\/tex] e [tex]\\dfrac{a-c}{b-d}=3[\/tex], com [tex]a,b,c[\/tex] e [tex]d[\/tex] distintos dois a dois. Calcule o valor de [tex]\\dfrac{a-d}{b-c}.[\/tex] Solu\u00e7\u00e3o Observe, inicialmente que: de [tex]\\dfrac{a-b}{c-d}=2[\/tex], segue que: [tex]\\qquad a-b=2c-2d[\/tex] [tex]\\qquad a+2d=b+2c;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\textcolor{#800000}{(i)}[\/tex] de [tex]\\dfrac{a-c}{b-d}=3[\/tex], segue que: [tex]\\qquad a-c=3b-3d[\/tex] [tex]\\qquad a+3d=3b+c.\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\textcolor{#800000}{(ii)}[\/tex] Multiplicando &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/problema-calcule-o-valor\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":721,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-141227","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/141227","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/721"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=141227"}],"version-history":[{"count":18,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/141227\/revisions"}],"predecessor-version":[{"id":193882,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/141227\/revisions\/193882"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=141227"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}