{"id":14467,"date":"2018-04-14T00:00:42","date_gmt":"2018-04-13T23:00:42","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14467"},"modified":"2022-01-07T21:41:54","modified_gmt":"2022-01-07T21:41:54","slug":"resolve-cada-uma-das-seguintes-equacoes-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14467","title":{"rendered":"Resolve cada uma das seguintes equa\u00e7\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_14467' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14467' class='GTTabs_curr'><a  id=\"14467_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14467' ><a  id=\"14467_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_14467'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Resolve cada uma das seguintes equa\u00e7\u00f5es, tendo em aten\u00e7\u00e3o as sugest\u00f5es dadas:<\/p>\n<ol>\n<li>\\(0,1{x^2} &#8211; 1,4x + 4,8 = 0\\)<br \/>\nSugest\u00e3o: Multiplica ambos os membros da equa\u00e7\u00e3o por 10.<\/li>\n<li>\\(\\frac{{{x^2}}}{9} &#8211; \\frac{x}{2} = \\frac{x}{9} + \\frac{1}{3}\\)<br \/>\nSugest\u00e3o: Multiplica ambos os membros da equa\u00e7\u00e3o por 18.<\/li>\n<li>\\( &#8211; 5{x^2} + 30x = 50 &#8211; 5x\\)<br \/>\nSugest\u00e3o: Depois de escreveres a equa\u00e7\u00e3o na forma can\u00f3nica, divide ambos os membros por \\( &#8211; 5\\).<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14467' onClick='GTTabs_show(1,14467)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14467'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{0,1{x^2} &#8211; 1,4x + 4,8 = 0}&amp; \\Leftrightarrow &amp;{{x^2} &#8211; 14x + 48 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{14 \\mp \\sqrt {{{\\left( { &#8211; 14} \\right)}^2} &#8211; 4 \\times 1 \\times 48} }}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{14 \\mp \\sqrt 4 }}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = \\frac{{14 &#8211; 2}}{2}}&amp; \\vee &amp;{x = \\frac{{14 + 2}}{2}}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 6}&amp; \\vee &amp;{x = 8}\\end{array}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left\\{ {6,\\;8} \\right\\}}\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{\\frac{{{x^2}}}{{\\mathop 9\\limits_{\\left( 2 \\right)} }} &#8211; \\frac{x}{{\\mathop 2\\limits_{\\left( 9 \\right)} }} = \\frac{x}{{\\mathop 9\\limits_{\\left( 2 \\right)} }} + \\frac{1}{{\\mathop 3\\limits_{\\left( 6 \\right)} }}}&amp; \\Leftrightarrow &amp;{2{x^2} &#8211; 9x = 2x + 6}\\\\{}&amp; \\Leftrightarrow &amp;{2{x^2} &#8211; 11x &#8211; 6 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{11 \\mp \\sqrt {{{\\left( { &#8211; 11} \\right)}^2} &#8211; 4 \\times 2 \\times \\left( { &#8211; 6} \\right)} }}{{2 \\times 2}}}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{11 \\mp \\sqrt {169} }}{4}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = \\frac{{11 &#8211; 13}}{4}}&amp; \\vee &amp;{x = \\frac{{11 + 13}}{4}}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; \\frac{1}{2}}&amp; \\vee &amp;{x = 6}\\end{array}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left\\{ { &#8211; \\frac{1}{2},\\;6} \\right\\}}\\end{array}\\]<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{ &#8211; 5{x^2} + 30x = 50 &#8211; 5x}&amp; \\Leftrightarrow &amp;{ &#8211; 5{x^2} + 35x &#8211; 50 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{{x^2} &#8211; 7x + 10 = 0}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{7 \\mp \\sqrt {{{\\left( { &#8211; 7} \\right)}^2} &#8211; 4 \\times 1 \\times 10} }}{{2 \\times 1}}}\\\\{}&amp; \\Leftrightarrow &amp;{x = \\frac{{7 \\mp \\sqrt 9 }}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = \\frac{{7 &#8211; 3}}{2}}&amp; \\vee &amp;{x = \\frac{{7 + 3}}{2}}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 2}&amp; \\vee &amp;{x = 5}\\end{array}}\\\\{}&amp;{}&amp;{}\\\\{}&amp;{}&amp;{S = \\left\\{ {2,\\;5} \\right\\}}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14467' onClick='GTTabs_show(0,14467)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolve cada uma das seguintes equa\u00e7\u00f5es, tendo em aten\u00e7\u00e3o as sugest\u00f5es dadas: \\(0,1{x^2} &#8211; 1,4x + 4,8 = 0\\) Sugest\u00e3o: Multiplica ambos os membros da equa\u00e7\u00e3o por 10. \\(\\frac{{{x^2}}}{9} &#8211; \\frac{x}{2}&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14061,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,306,304],"series":[],"class_list":["post-14467","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","tag-formula-resolvente"],"views":1831,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat06.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14467","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=14467"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14467\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14061"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14467"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14467"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14467"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14467"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}