{"id":24789,"date":"2023-04-03T17:57:01","date_gmt":"2023-04-03T16:57:01","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24789"},"modified":"2023-04-03T18:45:40","modified_gmt":"2023-04-03T17:45:40","slug":"resolve-as-seguintes-equacoes-4","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24789","title":{"rendered":"Resolve as seguintes equa\u00e7\u00f5es"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24789' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24789' class='GTTabs_curr'><a  id=\"24789_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24789' ><a  id=\"24789_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_24789'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Resolve as seguintes equa\u00e7\u00f5es:<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 3.51563%;\">a)<\/td>\n<td style=\"width: 96.3542%; text-align: left;\">\\(4{x^2} = 81\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.51563%;\">b)<\/td>\n<td style=\"width: 96.3542%; text-align: left;\">\\(27 &#8211; 3{x^2} = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.51563%;\">c)<\/td>\n<td style=\"width: 96.3542%; text-align: left;\">\\({\\left( {x &#8211; 4} \\right)^2} + 9 = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.51563%;\">d)<\/td>\n<td style=\"width: 96.3542%; text-align: left;\">\\({\\left( {x + 3} \\right)^2} &#8211; 4 = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.51563%;\">e)<\/td>\n<td style=\"width: 96.3542%; text-align: left;\">\\({x^2} &#8211; 7 = 5{x^2} &#8211; 7\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.51563%;\">f)<\/td>\n<td style=\"width: 96.3542%; text-align: left;\">\\(16{x^2} &#8211; {\\left( {x &#8211; 1} \\right)^2} = 0\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24789' onClick='GTTabs_show(1,24789)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24789'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Segue a resolu\u00e7\u00e3o das equa\u00e7\u00f5es.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 3.51563%;\">a)<\/td>\n<td style=\"width: 48.1771%; text-align: left;\">\\[\\begin{array}{*{20}{l}}{4{x^2} = 81}&amp; \\Leftrightarrow &amp;{{x^2} = \\frac{{81}}{4}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; \\frac{9}{2}}&amp; \\vee &amp;{x = \\frac{9}{2}}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"width: 48.1771%; text-align: left;\">\\[S = \\left\\{ { &#8211; \\frac{9}{2},\\;\\frac{9}{2}} \\right\\}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.51563%;\">b)<\/td>\n<td style=\"width: 48.1771%; text-align: left;\">\\[\\begin{array}{*{20}{l}}{27 &#8211; 3{x^2} = 0}&amp; \\Leftrightarrow &amp;{ &#8211; 3{x^2} = &#8211; 27}\\\\{}&amp; \\Leftrightarrow &amp;{{x^2} = 9}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 3}&amp; \\vee &amp;{x = 3}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"width: 48.1771%; text-align: left;\">\\[S = \\left\\{ { &#8211; 3,\\;3} \\right\\}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.51563%;\">c)<\/td>\n<td style=\"width: 48.1771%; text-align: left;\">\\[\\begin{array}{*{20}{l}}{{{\\left( {x &#8211; 4} \\right)}^2} + 9 = 0}&amp; \\Leftrightarrow &amp;{{{\\left( {x &#8211; 4} \\right)}^2} = &#8211; 9}\\\\{}&amp; \\Leftrightarrow &amp;{x \\in \\emptyset }\\\\{}&amp;{}&amp;{{\\rm{A\\;equa\u00e7\u00e3o\\;\u00e9\\;imposs\u00edvel}}}\\end{array}\\]<\/td>\n<td style=\"width: 48.1771%; text-align: left;\">\\[S = \\left\\{ {} \\right\\}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.51563%;\">d)<\/td>\n<td style=\"width: 48.1771%; text-align: left;\">\\[\\begin{array}{*{20}{l}}{{{\\left( {x + 3} \\right)}^2} &#8211; 4 = 0}&amp; \\Leftrightarrow &amp;{{{\\left( {x + 3} \\right)}^2} = 4}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x + 3 = &#8211; 2}&amp; \\vee &amp;{x + 3 = 2}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 5}&amp; \\vee &amp;{x = &#8211; 1}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"width: 48.1771%; text-align: left;\">\\[S = \\left\\{ { &#8211; 5,\\; &#8211; 1} \\right\\}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.51563%;\">e)<\/td>\n<td style=\"width: 48.1771%; text-align: left;\">\\[\\begin{array}{*{20}{l}}{{x^2} &#8211; 7 = 5{x^2} &#8211; 7}&amp; \\Leftrightarrow &amp;{{x^2} = 5{x^2}}\\\\{}&amp; \\Leftrightarrow &amp;{4{x^2} = 0}\\\\{}&amp; \\Leftrightarrow &amp;{{x^2} = 0}\\\\{}&amp; \\Leftrightarrow &amp;{x = 0}\\end{array}\\]<\/td>\n<td style=\"width: 48.1771%; text-align: left;\">\\[S = \\left\\{ 0 \\right\\}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.51563%;\">f)<\/td>\n<td style=\"width: 48.1771%; text-align: left;\">\\[\\begin{array}{*{20}{l}}{16{x^2} &#8211; {{\\left( {x &#8211; 1} \\right)}^2} = 0}&amp; \\Leftrightarrow &amp;{{{\\left( {4x} \\right)}^2} &#8211; {{\\left( {x &#8211; 1} \\right)}^2} = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\left( {4x + \\left( {x &#8211; 1} \\right)} \\right)\\left( {4x &#8211; \\left( {x &#8211; 1} \\right)} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\left( {5x &#8211; 1} \\right)\\left( {3x + 1} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{5x &#8211; 1 = 0}&amp; \\vee &amp;{3x + 1 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = \\frac{1}{5}}&amp; \\vee &amp;{x = &#8211; \\frac{1}{3}}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"width: 48.1771%; text-align: left;\">\\[S = \\left\\{ { &#8211; \\frac{1}{3},\\;\\frac{1}{5}} \\right\\}\\]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u00a0<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24789' onClick='GTTabs_show(0,24789)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolve as seguintes equa\u00e7\u00f5es: a) \\(4{x^2} = 81\\) b) \\(27 &#8211; 3{x^2} = 0\\) c) \\({\\left( {x &#8211; 4} \\right)^2} + 9 = 0\\) d) \\({\\left( {x + 3} \\right)^2} &#8211;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19189,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,706,198],"series":[],"class_list":["post-24789","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-monomios-e-polinomios","tag-8-o-ano","tag-equacao-incompleta-do-2-o-grau","tag-lei-do-anulamento-do-produto"],"views":82,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat75.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24789","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=24789"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24789\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24789"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24789"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24789"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}