{"id":41379,"date":"2015-06-30T17:10:44","date_gmt":"2015-06-30T20:10:44","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=41379"},"modified":"2023-03-22T23:20:18","modified_gmt":"2023-03-23T02:20:18","slug":"determine-x","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/determine-x\/","title":{"rendered":".Problema de Gincana:   Determine x"},"content":{"rendered":"<p style=\"margin:20px\">\n<div class=\"g1n\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\">Problema<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nSabendo que  [tex] \\, 4x \\, [\/tex] \u00e9 o inverso multiplicativo de [tex] \\, \\dfrac{1}{x^3} \\, [\/tex], <strong>determine [tex] \\, x \\, [\/tex]<\/strong>. <\/p>\n<p style=\"margin:20px\">\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g1n\">\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: 10px; margin-bottom: 20px;border: 0 none\"\/>\nDo enunciado temos que [tex]4x \\cdot  \\dfrac{1}{x^3} = 1  [\/tex] e, tamb\u00e9m, uma sutileza: a raz\u00e3o [tex] \\, \\dfrac{1}{x^3} \\, [\/tex] existe, logo [tex] \\, x\\ne 0 \\, [\/tex].<br \/>\n\tAssim, temos garantidas as seguintes equival\u00eancias:<br \/>\n\t[tex]\\qquad 4x \\cdot  \\dfrac{1}{x^3} = 1\\iff \\dfrac{4x}{x^3} = 1 \\iff \\dfrac{4}{x^2} = 1 \\iff x^2 = 4 \\iff x=\\pm 2[\/tex].<br \/>\n\tPortanto, existem dois poss\u00edveis valores para [tex] \\, x \\, [\/tex]: [tex] \\, x=2 \\, [\/tex] ou [tex] \\, x=-2 \\, [\/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>.<\/span><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"gg\">\nPrimeira Gincana de 2015 &#8211; Clubes de Matem\u00e1tica da OBMEP<br \/>\nN\u00edvel A &#8211; Quest\u00e3o M\u00e9dia<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Problema Sabendo que [tex] \\, 4x \\, [\/tex] \u00e9 o inverso multiplicativo de [tex] \\, \\dfrac{1}{x^3} \\, [\/tex], determine [tex] \\, x \\, [\/tex]. Solu\u00e7\u00e3o Do enunciado temos que [tex]4x \\cdot \\dfrac{1}{x^3} = 1 [\/tex] e, tamb\u00e9m, uma sutileza: a raz\u00e3o [tex] \\, \\dfrac{1}{x^3} \\, [\/tex] existe, logo [tex] \\, x\\ne 0 \\, [\/tex]. Assim, &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/determine-x\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-41379","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/41379","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\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=41379"}],"version-history":[{"count":26,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/41379\/revisions"}],"predecessor-version":[{"id":185122,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/41379\/revisions\/185122"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=41379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}