{"id":19248,"date":"2014-05-23T12:43:47","date_gmt":"2014-05-23T15:43:47","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=19248"},"modified":"2023-02-01T01:20:30","modified_gmt":"2023-02-01T04:20:30","slug":"probleminha-em-busca-do-digito-perdido","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/probleminha-em-busca-do-digito-perdido\/","title":{"rendered":".Probleminha: Em busca do d\u00edgito perdido"},"content":{"rendered":"<p style=\"margin:10px\">\n<div class=\"g1n\">\n<p class=\"tit\" \n\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\"\/>\nEncontre o n\u00famero positivo [tex]t[\/tex] e o d\u00edgito [tex]a[\/tex] que aparecem na igualdade:<\/p>\n<p style=\"text-align: center;margin:10px\">\n[tex][3(230+t)]^2= 492a04[\/tex].<\/p>\n<\/div>\n<p style=\"margin:40px\">\n<div class=\"g1n\">\n<p class=\"tit\" \n\n<p class=\"tit\" style=\"line-height:25px;margin:10px\">Solu\u00e7\u00e3o 1<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicada a partir do 7\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<strong>[3(230+1)]<sup>2<\/sup> = [3*231]<sup>2<\/sup>=[693]<sup>2<\/sup>=480249<br \/>\n[3(230+2)]<sup>2<\/sup> = [3*232]<sup>2<\/sup>=[696]<sup>2<\/sup>=484416<br \/>\n[3(230+3)]<sup>2<\/sup> = [3*233]<sup>2<\/sup>=[699]<sup>2<\/sup>488601<br \/>\n[3(230+4)]<sup>2<\/sup> = [3*234]<sup>2<\/sup>=[702]<sup>2<\/sup>=492804 <\/strong><br \/>\n<strong> t = 4<\/strong>  e<strong> a= 8<\/strong>.<\/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 pelo Clube <strong> MIRIM APRENDIZ<\/strong>. <\/p>\n<\/div>\n<p style=\"margin:40px\">\n<div class=\"g1n\">\n<p class=\"tit\" \n\n<p class=\"tit\" style=\"line-height:25px;margin:10px\">Solu\u00e7\u00e3o 2<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicada 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 O lado esquerdo da igualdade \u00e9 divis\u00edvel por [tex]9[\/tex] e, consequentemente, o lado direito tamb\u00e9m. Desse modo, a soma dos algarismos do lado direito \u00e9 divis\u00edvel por [tex]9[\/tex], o que ocorre apenas se [tex]a=8[\/tex].<br \/>\nAssim, segue que<br \/>\n[tex]\\qquad \\qquad [3(230+t)]^2= 492804 \\\\<br \/>\n\\qquad \\qquad (230+t)^2 = \\frac{492804}{9} \\\\<br \/>\n\\qquad \\qquad 230+t=\\sqrt{54756}\\\\<br \/>\n\\qquad \\qquad230+t=234.[\/tex]<br \/>\nPortanto, [tex]a=8[\/tex] e [tex]t=4[\/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> .<\/p>\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g3\" style=\"width: 430px;\"> Participou da discuss\u00e3o o Clube <strong>MIRIM APRENDIZ<\/strong>.<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":166,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-19248","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/19248","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\/166"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=19248"}],"version-history":[{"count":25,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/19248\/revisions"}],"predecessor-version":[{"id":183688,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/19248\/revisions\/183688"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=19248"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}