{"id":11659,"date":"2013-11-18T00:59:15","date_gmt":"2013-11-18T02:59:15","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=11659"},"modified":"2023-01-07T22:40:21","modified_gmt":"2023-01-08T01:40:21","slug":"problema-todos-os-texxtex-reais","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problema-todos-os-texxtex-reais\/","title":{"rendered":".Problema: Todos os [tex]x[\/tex] reais"},"content":{"rendered":"<div style=\"border: 3px solid #800000; padding: 8px;text-align: justify; font-family: verdana; color: #616161; line-height: 20px;\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\"><strong>Problema<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicado a partir do 9\u00ba ano do E. F.)<\/span><\/strong><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nEncontre todos os n\u00fameros reais [tex]x[\/tex] tais que<br \/>\n&nbsp;<br \/>\n[tex]\\qquad \\qquad (x+1995) (x+1997) (x+1999) (x+2001)+16=0\\,.[\/tex]<br \/>\n&nbsp;\n<\/div>\n<p>&nbsp;<\/p>\n<div style=\"border: 3px  solid  #800000; padding: 8px;\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\"><strong>Solu\u00e7\u00e3o <\/strong><\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\n<p style=\"text-align: justify; padding-left: 12px;\"><span style=\"font-family: verdana; color: #616161; line-height: 20px;\"> Fa\u00e7a [tex]x+1998=y[\/tex]. Deste modo, a equa\u00e7\u00e3o dada pode ser reescrita como<br \/>\n&nbsp;<br \/>\n[tex]\\qquad (y-3) (y-1) (y+1) (y+3)+16=0 \\\\<br \/>\n\\qquad (y^2-9) (y^2-1)+16=0 \\\\<br \/>\n\\qquad  y^4-10y^2+9+16=0 \\\\<br \/>\n\\qquad y^4-10y^2+25=0 \\\\<br \/>\n\\qquad  (y^2-5)^2=0 \\\\<br \/>\n\\qquad  y^2-5=0 \\\\<br \/>\n\\qquad  y=\\pm \\sqrt{5}\\,.[\/tex]<br \/>\n&nbsp;<br \/>\nLogo, como [tex]x+1998=y[\/tex], segue que:<br \/>\n&nbsp;<br \/>\n[tex]\\qquad x+1998=\\pm \\sqrt{5} \\\\<br \/>\n\\qquad x=-1998\\pm \\sqrt{5}\\,.[\/tex]<br \/>\n&nbsp;<br \/>\nAssim, s\u00e3o dois os valores de [tex]x[\/tex]: [tex]\\boxed{x_1=-1998+\\sqrt{5}\\,}\\;[\/tex] e [tex]\\; \\boxed{x_2=-1998-\\sqrt{5}\\,}\\,.[\/tex]<br \/>\n<\/span><\/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>&nbsp;<\/p>\n<div style=\"border: 1px solid #616161; padding: 8px;\">\n<p style=\"text-align: justify;\"><span style=\"font-family: verdana; color: #616161;\" > Participou da discuss\u00e3o do problema o Clube <strong>Math Error.<\/strong><\/span><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Problema (Indicado a partir do 9\u00ba ano do E. F.) Encontre todos os n\u00fameros reais [tex]x[\/tex] tais que &nbsp; [tex]\\qquad \\qquad (x+1995) (x+1997) (x+1999) (x+2001)+16=0\\,.[\/tex] &nbsp; &nbsp; Solu\u00e7\u00e3o Fa\u00e7a [tex]x+1998=y[\/tex]. Deste modo, a equa\u00e7\u00e3o dada pode ser reescrita como &nbsp; [tex]\\qquad (y-3) (y-1) (y+1) (y+3)+16=0 \\\\ \\qquad (y^2-9) (y^2-1)+16=0 \\\\ \\qquad y^4-10y^2+9+16=0 \\\\ \\qquad y^4-10y^2+25=0 &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/problema-todos-os-texxtex-reais\/\">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-11659","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/11659","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=11659"}],"version-history":[{"count":17,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/11659\/revisions"}],"predecessor-version":[{"id":182743,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/11659\/revisions\/182743"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=11659"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}