{"id":301,"date":"2020-03-26T23:30:51","date_gmt":"2020-03-27T02:30:51","guid":{"rendered":"http:\/\/cinoto.com.br\/matematica\/?p=301"},"modified":"2020-03-26T23:30:51","modified_gmt":"2020-03-27T02:30:51","slug":"determine-m-tal-que-5cm132cm22","status":"publish","type":"post","link":"http:\/\/cinoto.com.br\/matematica\/determine-m-tal-que-5cm132cm22\/","title":{"rendered":"3) Determine m tal que 5.C(m+1, 3) = 2.C(m+2, 2), onde C(n, p) \u00e9 o n\u00famero de combina\u00e7\u00f5es de n elementos tomados p a p."},"content":{"rendered":"\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">Resolu\u00e7\u00e3o:<\/h2>\n\n\n<div>5.C(m+1, 3) = 2.C(m+2, 2)<\/div>\n<div>5.(m + 1)!\/3!.(m + 1 &#8211; 3)! = 2.(m + 2)!\/2!.(m + 2 &#8211; 2)!<\/div>\n<div>5.(m + 1)!\/3!.(m &#8211; 2)! = 2.(m + 2)!\/2!.m!<\/div>\n<div>5.(m + 1)!\/3!.(m &#8211; 2)! = (m + 2)!\/m!<\/div>\n<div>5.(m + 1)!\/3!.(m &#8211; 2)! = (m + 2).(m + 1)!\/m!<\/div>\n<div>\u00a0<\/div>\n<div>\n<div>divide os dois membros por (m + 1)!:<\/div>\n<div>5\/3!.(m &#8211; 2)! = (m + 2)\/m!<\/div>\n<div>5\/3!.(m &#8211; 2)! = (m + 2)\/m.(m &#8211; 1).(m &#8211; 2)!<\/div>\n<div>\u00a0<\/div>\n<div>multiplica os dois membros por (m &#8211; 2)!:<\/div>\n<div>5\/3! = (m + 2)\/m.(m &#8211; 1)<\/div>\n<div>5\/6 = (m + 2)\/m.(m &#8211; 1)<\/div>\n<div>5.m.(m &#8211; 1) = 6.(m + 2)<\/div>\n<div>5m\u00b2 &#8211; 5m = 6m + 12<\/div>\n<div>5m\u00b2 &#8211; 11m &#8211; 12 = 0<\/div>\n<div>\u00a0<\/div>\n<div>resolvendo a equa\u00e7\u00e3o do segundo grau:<\/div>\n<div>(5m + 4).(m &#8211; 3) = 0<\/div>\n<div>m = -4\/5 ou m = 3<\/div>\n<div>\u00a0<\/div>\n<div>Como m tem que ser um n\u00famero natural:<\/div>\n<div>m = 3<\/div>\n<\/div>","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-301","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\/301","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=301"}],"version-history":[{"count":1,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/posts\/301\/revisions"}],"predecessor-version":[{"id":302,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/posts\/301\/revisions\/302"}],"wp:attachment":[{"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/media?parent=301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/categories?post=301"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/tags?post=301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}