{"id":26131,"date":"2023-05-27T12:15:37","date_gmt":"2023-05-27T11:15:37","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26131"},"modified":"2023-05-27T12:21:58","modified_gmt":"2023-05-27T11:21:58","slug":"sabe-se-que-a-soma-de-dois-numeros-naturais-e-12","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26131","title":{"rendered":"Sabe-se que a soma de dois n\u00fameros naturais \u00e9 12"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26131' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26131' class='GTTabs_curr'><a  id=\"26131_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26131' ><a  id=\"26131_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_26131'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sabe-se que a soma de dois n\u00fameros naturais \u00e9 12 e a soma do dobro desses n\u00fameros \u00e9 14.<br \/>Quais s\u00e3o esses n\u00fameros?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26131' onClick='GTTabs_show(1,26131)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26131'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Sabe-se que a soma de dois n\u00fameros naturais \u00e9 12 e a soma do dobro desses n\u00fameros \u00e9 14.<br \/>Quais s\u00e3o esses n\u00fameros?<\/p>\n<\/blockquote>\n<p><br \/>Sejam <em>m<\/em> e <em>n<\/em> esses dois n\u00fameros naturais.<\/p>\n<p>Equacionando o problema e resolvendo o sistema de equa\u00e7\u00f5es, vem: \\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{m + n = 12}\\\\{2m + 2n = 14}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{m = 12 &#8211; n}\\\\{24 &#8211; 2n + 2n = 14}\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{0n = &#8211; 10}\\\\{m = 12 &#8211; n}\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{n \\in \\emptyset }\\\\{m \\in \\emptyset }\\end{array}} \\right.}&amp;{}&amp;{}&amp;{}\\end{array}\\]<\/p>\n<p>N\u00e3o h\u00e1 n\u00fameros nestas condi\u00e7\u00f5es, pois o sistema de equa\u00e7\u00f5es \u00e9 imposs\u00edvel.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26131' onClick='GTTabs_show(0,26131)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sabe-se que a soma de dois n\u00fameros naturais \u00e9 12 e a soma do dobro desses n\u00fameros \u00e9 14.Quais s\u00e3o esses n\u00fameros? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19173,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,714],"tags":[424,345,239],"series":[],"class_list":["post-26131","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-literais-e-sistemas","tag-8-o-ano","tag-funcao-afim","tag-sistema-de-equacoes"],"views":62,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat64.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26131","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=26131"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26131\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19173"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26131"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26131"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26131"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26131"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}