{"id":14395,"date":"2018-04-11T19:13:16","date_gmt":"2018-04-11T18:13:16","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14395"},"modified":"2022-01-06T23:04:46","modified_gmt":"2022-01-06T23:04:46","slug":"a-soma-de-uma-constante-com-o-quadrado-de-um-polinomio-de-1-o-grau","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14395","title":{"rendered":"A soma de uma constante com o quadrado de um polin\u00f3mio de 1.\u00ba grau"},"content":{"rendered":"<p><ul id='GTTabs_ul_14395' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14395' class='GTTabs_curr'><a  id=\"14395_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14395' ><a  id=\"14395_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_14395'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Obt\u00e9m, para cada al\u00ednea, uma express\u00e3o equivalente que seja a soma\u00a0de uma constante com o quadrado de um polin\u00f3mio de primeiro grau (eventualmente multiplicado por uma constante).<\/p>\n<ol>\n<li>\\({x^2} + 4x + 2\\)<\/li>\n<li>\\({x^2} &#8211; 6x &#8211; 1\\)<\/li>\n<li>\\({x^2} + x + 1\\)<\/li>\n<li>\\(3{x^2} + 2x + 7\\)<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14395' onClick='GTTabs_show(1,14395)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14395'>\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} + 4x + 2}&amp; = &amp;{{{\\left( {x + 2} \\right)}^2} &#8211; 4 + 2}\\\\{}&amp; = &amp;{{{\\left( {x + 2} \\right)}^2} &#8211; 2}\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{{x^2} &#8211; 6x &#8211; 1}&amp; = &amp;{{{\\left( {x &#8211; 3} \\right)}^2} &#8211; 9 &#8211; 1}\\\\{}&amp; = &amp;{{{\\left( {x &#8211; 3} \\right)}^2} &#8211; 10}\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{{x^2} + x + 1}&amp; = &amp;{{{\\left( {x + \\frac{1}{2}} \\right)}^2} &#8211; \\frac{1}{4} + 1}\\\\{}&amp; = &amp;{{{\\left( {x + \\frac{1}{2}} \\right)}^2} + \\frac{3}{4}}\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{3{x^2} + 2x + 7}&amp; = &amp;{3\\left( {{x^2} + \\frac{2}{3}x} \\right) + 7}\\\\{}&amp; = &amp;{3{{\\left( {x + \\frac{1}{3}} \\right)}^2} &#8211; \\frac{1}{9} \\times 3 + 7}\\\\{}&amp; = &amp;{3{{\\left( {x + \\frac{1}{3}} \\right)}^2} + \\frac{{20}}{3}}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14395' onClick='GTTabs_show(0,14395)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Obt\u00e9m, para cada al\u00ednea, uma express\u00e3o equivalente que seja a soma\u00a0de uma constante com o quadrado de um polin\u00f3mio de primeiro grau (eventualmente multiplicado por uma constante). \\({x^2} + 4x +&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14083,"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-14395","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":1696,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat28.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14395","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=14395"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14395\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14083"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14395"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14395"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14395"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14395"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}