{"id":8591,"date":"2012-04-19T21:46:03","date_gmt":"2012-04-19T20:46:03","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8591"},"modified":"2022-01-06T19:28:20","modified_gmt":"2022-01-06T19:28:20","slug":"resolve-as-equacoes-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8591","title":{"rendered":"Resolve as equa\u00e7\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_8591' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8591' class='GTTabs_curr'><a  id=\"8591_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8591' ><a  id=\"8591_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_8591'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Resolve as equa\u00e7\u00f5es:<\/p>\n<ol>\n<li>${\\sqrt 2 {x^2} + 11x = 0}$<\/li>\n<li>${x^2} + 9 = 0$<\/li>\n<li>$5a + {\\left( {a + 2} \\right)^2} = 3a\\left( {a + 2} \\right) + a$<\/li>\n<li>$4,8{x^2} &#8211; 8,4x + 2,4 = 0$<\/li>\n<li>$\\frac{{a &#8211; 1}}{2} &#8211; \\frac{{a\\left( {3 &#8211; a} \\right)}}{3} = a + \\frac{1}{3}$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8591' onClick='GTTabs_show(1,8591)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8591'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Resolvendo a equa\u00e7\u00e3o, vem:<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\sqrt 2 {x^2} + 11x = 0}&amp; \\Leftrightarrow &amp;{x\\left( {\\sqrt 2 x + 11} \\right) = 0} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{x = 0}&amp; \\vee &amp;{\\sqrt 2 x + 11 = 0}<br \/>\n\\end{array}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{x = 0}&amp; \\vee &amp;{x =\u00a0 &#8211; \\frac{{11}}{{\\sqrt 2 }}}<br \/>\n\\end{array}}<br \/>\n\\end{array}$$<\/li>\n<li>Resolvendo a equa\u00e7\u00e3o, vem:<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{{x^2} + 9 = 0}&amp; \\Leftrightarrow &amp;{\\overbrace {{x^2} =\u00a0 &#8211; 9}^{{\\text{Equa\u00e3o imposs\u00edvel}}}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{x \\in \\emptyset }<br \/>\n\\end{array}$$<\/li>\n<li>Resolvendo a equa\u00e7\u00e3o, vem:<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{5a + {{\\left( {a + 2} \\right)}^2} = 3a\\left( {a + 2} \\right) + a}&amp; \\Leftrightarrow &amp;{5a + {a^2} + 4a + 4 = 3{a^2} + 6a + a} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{2{a^2} &#8211; 2a &#8211; 4 = 0} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{{a^2} &#8211; a &#8211; 2 = 0} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{a = \\frac{{1 \\pm \\sqrt {{{( &#8211; 1)}^2} &#8211; 4 \\times 1 \\times ( &#8211; 2)} }}{2}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{a = \\frac{{1 \\pm 3}}{2}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{a =\u00a0 &#8211; 1}&amp; \\vee &amp;{a = 2}<br \/>\n\\end{array}}<br \/>\n\\end{array}$$<\/li>\n<li>Resolvendo a equa\u00e7\u00e3o, vem:<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{4,8{x^2} &#8211; 8,4x + 2,4 = 0}&amp; \\Leftrightarrow &amp;{4{x^2} &#8211; 7x + 2 = 0} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{x = \\frac{{7 \\pm \\sqrt {49 &#8211; 32} }}{8}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{x = \\frac{{7 \\pm \\sqrt {17} }}{8}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{x = \\frac{{7 &#8211; \\sqrt {17} }}{8}}&amp; \\vee &amp;{x = \\frac{{7 + \\sqrt {17} }}{8}}<br \/>\n\\end{array}}<br \/>\n\\end{array}$$<\/li>\n<li>Resolvendo a equa\u00e7\u00e3o, vem:<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\frac{{a &#8211; 1}}{{\\mathop 2\\limits_{(3)} }} &#8211; \\frac{{a\\left( {3 &#8211; a} \\right)}}{{\\mathop 3\\limits_{(2)} }} = \\mathop a\\limits_{(6)}\u00a0 + \\frac{1}{{\\mathop 3\\limits_{(2)} }}}&amp; \\Leftrightarrow &amp;{3a &#8211; 3 &#8211; 2a\\left( {3 &#8211; a} \\right) = 6a + 2} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{3a &#8211; 3 &#8211; 6a + 2{a^2} = 6a + 2} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{2{a^2} &#8211; 9a &#8211; 5 = 0} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{a = \\frac{{9 \\pm \\sqrt {81 + 40} }}{4}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{a = \\frac{{9 \\pm 11}}{4}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{a =\u00a0 &#8211; \\frac{1}{2}}&amp; \\vee &amp;{a = 5}<br \/>\n\\end{array}}<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8591' onClick='GTTabs_show(0,8591)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolve as equa\u00e7\u00f5es: ${\\sqrt 2 {x^2} + 11x = 0}$ ${x^2} + 9 = 0$ $5a + {\\left( {a + 2} \\right)^2} = 3a\\left( {a + 2} \\right) + a$ $4,8{x^2}&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19175,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,196,306,304,198],"series":[],"class_list":["post-8591","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-casos-notaveis","tag-equacao-do-2-o-grau","tag-formula-resolvente","tag-lei-do-anulamento-do-produto"],"views":2377,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat66.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8591","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=8591"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8591\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19175"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8591"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8591"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8591"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8591"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}