{"id":24602,"date":"2023-03-10T17:03:49","date_gmt":"2023-03-10T17:03:49","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24602"},"modified":"2023-03-10T18:10:09","modified_gmt":"2023-03-10T18:10:09","slug":"resolve-as-equacoes-4","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24602","title":{"rendered":"Resolve as equa\u00e7\u00f5es"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24602' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24602' class='GTTabs_curr'><a  id=\"24602_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24602' ><a  id=\"24602_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_24602'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<ol>\n<li>Resolve as equa\u00e7\u00f5es:<br \/>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 25%;\">\\(3{x^2} &#8211; 21 = 0\\)<\/td>\n<td style=\"width: 25%;\">\\({x^2} + 4 = 0\\)<\/td>\n<td style=\"width: 25%;\">\\({x^2} &#8211; 4 = 0\\)<\/td>\n<td style=\"width: 25%;\">\\(16 + 4{x^2} = 0\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Quando resolvemos uma equa\u00e7\u00e3o do 2.\u00ba grau do tipo \\(a{x^2} + c = 0\\) (\\(a \\ne 0\\)), encontramos sempre solu\u00e7\u00e3o?<br \/>Se n\u00e3o, quando \u00e9 que uma equa\u00e7\u00e3o deste tipo n\u00e3o tem solu\u00e7\u00e3o?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24602' onClick='GTTabs_show(1,24602)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24602'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Resolvendo as equa\u00e7\u00f5es, temos:<br \/><br \/>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td style=\"vertical-align: top;\">a)<\/td>\n<td style=\"text-align: left;\">\\(\\begin{array}{*{20}{l}}{3{x^2} &#8211; 21 = 0}&amp; \\Leftrightarrow &amp;{3{x^2} = 21}\\\\{}&amp; \\Leftrightarrow &amp;{{x^2} = 7}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; \\sqrt 7 }&amp; \\vee &amp;{x = \\sqrt 7 }\\end{array}}\\end{array}\\)<\/td>\n<td style=\"text-align: left;\">A equa\u00e7\u00e3o \u00e9 poss\u00edvel.<br \/>\\(S = \\left\\{ { &#8211; \\sqrt 7 ,\\sqrt 7 } \\right\\}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">b)<\/td>\n<td style=\"text-align: left;\">\\(\\begin{array}{*{20}{l}}{{x^2} + 4 = 0}&amp; \\Leftrightarrow &amp;{{x^2} = &#8211; 4}\\\\{}&amp; \\Leftrightarrow &amp;{x \\in \\emptyset }\\end{array}\\)<\/td>\n<td style=\"text-align: left;\">A equa\u00e7\u00e3o \u00e9 imposs\u00edvel.<br \/>\\(S = \\left\\{ {} \\right\\}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">c)<\/td>\n<td style=\"text-align: left;\">\\(\\begin{array}{*{20}{l}}{{x^2}&#8211;4 = 0}&amp; \\Leftrightarrow &amp;{{x^2} = 4}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 2}&amp; \\vee &amp;{x = 2}\\end{array}}\\end{array}\\)<\/td>\n<td style=\"text-align: left;\">A equa\u00e7\u00e3o \u00e9 poss\u00edvel.<br \/>\\(S = \\left\\{ { &#8211; 2,2} \\right\\}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"vertical-align: top;\">d)<\/td>\n<td style=\"text-align: left;\">\\(\\begin{array}{*{20}{l}}{16 + 4{x^2} = 0}&amp; \\Leftrightarrow &amp;{4{x^2} = &#8211; 16}\\\\{}&amp; \\Leftrightarrow &amp;{{x^2} = &#8211; 4}\\\\{}&amp; \\Leftrightarrow &amp;{x \\in \\emptyset }\\end{array}\\)<\/td>\n<td style=\"text-align: left;\">A equa\u00e7\u00e3o \u00e9 imposs\u00edvel.<br \/>\\(S = \\left\\{ {} \\right\\}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Quando resolvemos uma equa\u00e7\u00e3o do 2.\u00ba grau do tipo \\(a{x^2} + c = 0\\) (\\(a \\ne 0\\)), nem sempre encontramos solu\u00e7\u00e3o. Com efeito:<br \/>\\[\\begin{array}{*{20}{l}}{a{x^2} + c = 0}&amp; \\Leftrightarrow &amp;{a{x^2} = &#8211; c}\\\\{}&amp; \\Leftrightarrow &amp;{{x^2} = &#8211; \\frac{c}{a}}\\end{array}\\]<br \/>Uma equa\u00e7\u00e3o deste tipo n\u00e3o tem solu\u00e7\u00e3o quando \\(\\frac{c}{a} &gt; 0\\), isto \u00e9, quando \\(a\\) e \\(c\\) s\u00e3o do mesmo sinal.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24602' onClick='GTTabs_show(0,24602)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolve as equa\u00e7\u00f5es: \\(3{x^2} &#8211; 21 = 0\\) \\({x^2} + 4 = 0\\) \\({x^2} &#8211; 4 = 0\\) \\(16 + 4{x^2} = 0\\) Quando resolvemos uma equa\u00e7\u00e3o do 2.\u00ba grau do&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14114,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,706,705],"series":[],"class_list":["post-24602","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-polinomios"],"views":119,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat56.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24602","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=24602"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24602\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24602"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24602"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24602"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24602"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}