{"id":14495,"date":"2018-04-14T18:20:17","date_gmt":"2018-04-14T17:20:17","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14495"},"modified":"2022-01-07T22:04:36","modified_gmt":"2022-01-07T22:04:36","slug":"dois-numeros-inteiros-consecutivos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14495","title":{"rendered":"Dois n\u00fameros inteiros consecutivos"},"content":{"rendered":"<p><ul id='GTTabs_ul_14495' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14495' class='GTTabs_curr'><a  id=\"14495_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14495' ><a  id=\"14495_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_14495'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Averigua se existem dois n\u00fameros inteiros consecutivos de tal modo que o quadrado da sua soma seja 36.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14495' onClick='GTTabs_show(1,14495)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14495'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Averigua se existem dois n\u00fameros inteiros consecutivos de tal modo que o quadrado da sua soma seja 36.<\/p>\n<\/blockquote>\n<p>\u00adSeja \\(p \\in \\mathbb{Z}\\).<\/p>\n<p>Pretendemos saber se tem solu\u00e7\u00f5es, no conjunto dos inteiros, a equa\u00e7\u00e3o\u00a0\\({\\left( {p + p + 1} \\right)^2} = 36\\).<\/p>\n<p>Averiguemos o que se passa:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\begin{array}{*{20}{c}}{{{\\left( {p + p + 1} \\right)}^2} = 36}&amp; \\wedge &amp;{p \\in \\mathbb{Z}}\\end{array}}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{{{\\left( {2p + 1} \\right)}^2} = 36}&amp; \\wedge &amp;{p \\in \\mathbb{Z}}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{\\left( {\\begin{array}{*{20}{c}}{2p + 1 = &#8211; 6}&amp; \\vee &amp;{2p + 1 = 6}\\end{array}} \\right)}&amp; \\wedge &amp;{p \\in \\mathbb{Z}}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{\\left( {\\begin{array}{*{20}{c}}{p = &#8211; \\frac{7}{2}}&amp; \\vee &amp;{p = \\frac{5}{2}}\\end{array}} \\right)}&amp; \\wedge &amp;{p \\in \\mathbb{Z}}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{p \\in \\left\\{ {} \\right\\}}\\end{array}\\]<\/p>\n<p>Portanto, n\u00e3o\u00a0existem dois n\u00fameros inteiros consecutivos de tal modo que o quadrado da sua soma seja 36.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14495' onClick='GTTabs_show(0,14495)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Averigua se existem dois n\u00fameros inteiros consecutivos de tal modo que o quadrado da sua soma seja 36. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14093,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,306],"series":[],"class_list":["post-14495","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-equacoes-do-2-o-grau","tag-9-o-ano","tag-equacao-do-2-o-grau"],"views":3153,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat38.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14495","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=14495"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14495\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14093"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14495"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14495"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14495"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}