{"id":297,"date":"2020-03-26T23:27:02","date_gmt":"2020-03-27T02:27:02","guid":{"rendered":"http:\/\/cinoto.com.br\/matematica\/?p=297"},"modified":"2020-03-26T23:27:02","modified_gmt":"2020-03-27T02:27:02","slug":"resolva-x-2x-23-2-x-1-x-391","status":"publish","type":"post","link":"http:\/\/cinoto.com.br\/matematica\/resolva-x-2x-23-2-x-1-x-391\/","title":{"rendered":"1) Resolva: x!\/(2!(x-2)!) + (3\/2).(x-1)!\/(x &#8211; 3)! = 91"},"content":{"rendered":"\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">Resolu\u00e7\u00e3o:<\/h2>\n\n\n\n<p>Resolu\u00e7\u00e3o:<\/p>\n\n\n\n<p>Podemos expandir x! em x! = x.(x &#8211; 1).(x &#8211; 2)!, assim como (x &#8211; 1)! = (x &#8211; 1).(x &#8211; 2).(x &#8211; 3)!, ent\u00e3o temos:<\/p>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; x! &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3 &nbsp; &nbsp; (x &#8211; 1)!<br>&#8212;&#8212;&#8212;- + &#8212; . &#8212;&#8212;&#8212; = 91<br>&nbsp;2!(x-2)! &nbsp; &nbsp; 2 &nbsp; &nbsp; (x &#8211; 3)!<\/p>\n\n\n\n<p>x.(x-1).(x-2)! &nbsp; &nbsp;3 &nbsp; (x-1).(x-2).(x-3)!<br>&#8212;&#8212;&#8212;&#8212;&#8212;- + &#8211; . &#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8211; = 91<br>&nbsp; &nbsp; &nbsp;2!(x-2) ! &nbsp; &nbsp; &nbsp; 2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (x-3)!<\/p>\n\n\n\n<p>Simplificando:<\/p>\n\n\n\n<p>x.(x-1) &nbsp; &nbsp;3 &nbsp; (x-1).(x-2)<br>&#8212;&#8212;&#8211; + &#8211; . &#8212;&#8212;&#8212;&#8212;- = 91<br>&nbsp; &nbsp; 2! &nbsp; &nbsp; &nbsp; 2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1<\/p>\n\n\n\n<p>x.(x-1) &nbsp; 3.(x-1).(x-2) &nbsp; 182<br>&#8212;&#8212;&#8211; + &#8212;&#8212;&#8212;&#8212;&#8211; = &#8212;&#8211;<br>&nbsp; &nbsp; &nbsp;2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 2 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2<\/p>\n\n\n\n<p>x.(x-1) + 3.(x-1).(x-2) = 182<\/p>\n\n\n\n<p>x<sup>2<\/sup>&nbsp;&#8211; x + 3.(x<sup>2<\/sup>&nbsp;&#8211; 3x + 2) = 182<\/p>\n\n\n\n<p>x<sup>2<\/sup>&nbsp;&#8211; x + 3x<sup>2<\/sup>&nbsp;&#8211; 9x + 6 = 182<\/p>\n\n\n\n<p>4x<sup>2<\/sup>&nbsp;&#8211; 10x &#8211; 176 = 0<\/p>\n\n\n\n<p>2x<sup>2<\/sup>&nbsp;&#8211; 5x &#8211; 88 = 0<\/p>\n\n\n\n<p>Resolvendo essa equa\u00e7\u00e3o pela f\u00f3mula de B\u00e1skara voc\u00ea encontrar\u00e1 as seguintes ra\u00edzes:&nbsp;x = -11\/2 ou x = 8, que voc\u00ea tamb\u00e9m pode encontrar fatorando:<\/p>\n\n\n\n<p>2x<sup>2<\/sup>&nbsp;&#8211; 5x &#8211; 88 = 0<\/p>\n\n\n\n<p>(2x + 11).(x &#8211; 8) = 0<\/p>\n\n\n\n<p>x = -11\/2 ou x = 8<\/p>\n\n\n\n<p>Como estamos trabalhando com n\u00fameros fatoriais, x s\u00f3 pode ser inteiro e positivo. Ent\u00e3o&#8230;<\/p>\n\n\n\n<p>Resposta: x = 8<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[28],"class_list":["post-297","post","type-post","status-publish","format-standard","hentry","category-fatorial","tag-facil"],"_links":{"self":[{"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/posts\/297","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/comments?post=297"}],"version-history":[{"count":1,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/posts\/297\/revisions"}],"predecessor-version":[{"id":298,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/posts\/297\/revisions\/298"}],"wp:attachment":[{"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/media?parent=297"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/categories?post=297"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/tags?post=297"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}