{"id":220364,"date":"2024-07-30T18:12:29","date_gmt":"2024-07-30T21:12:29","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=220364"},"modified":"2024-07-30T18:15:11","modified_gmt":"2024-07-30T21:15:11","slug":"problemao-valor-da-expressao","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problemao-valor-da-expressao\/","title":{"rendered":".Problem\u00e3o: Valor da Express\u00e3o"},"content":{"rendered":"<p style=\"margin:10px\">\n<div class=\"g1n\" style=\"line-height:25px;padding-bottom:15px\">\n<p class=\"tit\" style=\"line-height:25px;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: 10px; margin-bottom: 20px;border: 0 none\"\/>\n<p>Sabendo que [tex]x^3+4x-8=0[\/tex], determine o valor num\u00e9rico de [tex]x^7+64x^2[\/tex].<\/p>\n<p style=\"font-size: 12px;text-align:right;line-height:1px;\">Extra\u00eddo de <strong>Instagram Sorunum_zoru<\/strong>.<\/p>\n<\/div>\n<p style=\"margin:40px\">\n<div class=\"g1n\" style=\"line-height:28px;\">\n<p class=\"tit\" style=\"line-height:28px;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>Inicialmente, perceba que [tex]x^3+4x-8=0 \\iff x^3=8-4x[\/tex].<br \/>\nDesse modo, temos:<br \/>\n[tex]\\qquad x^7+64x^2=x \\cdot x^6+64x^2[\/tex]<br \/>\n[tex]\\qquad\\qquad =x \\cdot (x^3)^2+64x^2[\/tex]<br \/>\n[tex]\\qquad\\qquad =x \\cdot (8-4x)^2+64x^2[\/tex]<br \/>\n[tex]\\qquad\\qquad =x \\cdot (8^2-2 \\cdot 8 \\cdot 4x+(4x)^2)+64x^2[\/tex]<br \/>\n[tex]\\qquad\\qquad =x \\cdot (64-64x+16x^2)+64x^2[\/tex]<br \/>\n[tex]\\qquad\\qquad =64x-64x^2+16x^3+64x^2[\/tex]<br \/>\n[tex]\\qquad\\qquad = 64x+16x^3[\/tex]<br \/>\n[tex]\\qquad\\qquad =16 \\cdot (4x+x^3)[\/tex]<br \/>\n[tex]\\qquad\\qquad = 16 \\cdot(4x+8-4x)=16 \\cdot 8=128[\/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\" >Solu\u00e7\u00e3o elaborada pelos <strong>Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Problema (Indicado a partir do 9\u00ba ano do E. F.) Sabendo que [tex]x^3+4x-8=0[\/tex], determine o valor num\u00e9rico de [tex]x^7+64x^2[\/tex]. Extra\u00eddo de Instagram Sorunum_zoru. Solu\u00e7\u00e3o Inicialmente, perceba que [tex]x^3+4x-8=0 \\iff x^3=8-4x[\/tex]. Desse modo, temos: [tex]\\qquad x^7+64x^2=x \\cdot x^6+64x^2[\/tex] [tex]\\qquad\\qquad =x \\cdot (x^3)^2+64x^2[\/tex] [tex]\\qquad\\qquad =x \\cdot (8-4x)^2+64x^2[\/tex] [tex]\\qquad\\qquad =x \\cdot (8^2-2 \\cdot 8 \\cdot 4x+(4x)^2)+64x^2[\/tex] [tex]\\qquad\\qquad =x &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/problemao-valor-da-expressao\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":164,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-220364","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/220364","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\/164"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=220364"}],"version-history":[{"count":6,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/220364\/revisions"}],"predecessor-version":[{"id":221795,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/220364\/revisions\/221795"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=220364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}