{"id":14396,"date":"2018-04-11T19:33:01","date_gmt":"2018-04-11T18:33:01","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14396"},"modified":"2022-01-06T23:07:16","modified_gmt":"2022-01-06T23:07:16","slug":"utilizando-o-completamento-do-quadrado","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14396","title":{"rendered":"Utilizando o completamento do quadrado"},"content":{"rendered":"<p><ul id='GTTabs_ul_14396' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14396' class='GTTabs_curr'><a  id=\"14396_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14396' ><a  id=\"14396_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_14396'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Resolve as equa\u00e7\u00f5es do 2.\u00ba grau, utilizando o completamento do quadrado.<\/p>\n<ol>\n<li>\\({{x^2} &#8211; 6x + 5 = 0}\\)<\/li>\n<li>\\({{x^2} + 5x + 1 = 0}\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14396' onClick='GTTabs_show(1,14396)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14396'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{{x^2} &#8211; 6x + 5 = 0}&amp; \\Leftrightarrow &amp;{{{\\left( {x &#8211; 3} \\right)}^2} &#8211; 9 + 5 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{{{\\left( {x &#8211; 3} \\right)}^2} = 4}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x &#8211; 3 = &#8211; 2}&amp; \\vee &amp;{x &#8211; 3 = 2}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 1}&amp; \\vee &amp;{x = 5}\\end{array}}\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{{x^2} + 5x + 1 = 0}&amp; \\Leftrightarrow &amp;{{{\\left( {x + \\frac{5}{2}} \\right)}^2} &#8211; \\frac{{25}}{4} + 1 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{{{\\left( {x + \\frac{5}{2}} \\right)}^2} = \\frac{{21}}{4}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x + \\frac{5}{2} = &#8211; \\frac{{\\sqrt {21} }}{2}}&amp; \\vee &amp;{x + \\frac{5}{2} = \\frac{{\\sqrt {21} }}{2}}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = \\frac{{ &#8211; 5 &#8211; \\sqrt {21} }}{2}}&amp; \\vee &amp;{x = \\frac{{ &#8211; 5 + \\sqrt {21} }}{2}}\\end{array}}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14396' onClick='GTTabs_show(0,14396)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolve as equa\u00e7\u00f5es do 2.\u00ba grau, utilizando o completamento do quadrado. \\({{x^2} &#8211; 6x + 5 = 0}\\) \\({{x^2} + 5x + 1 = 0}\\) Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14111,"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-14396","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":3246,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat53.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14396","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=14396"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14396\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14111"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14396"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14396"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14396"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}