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{"id":24804,"date":"2023-04-04T10:33:25","date_gmt":"2023-04-04T09:33:25","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24804"},"modified":"2023-04-04T11:07:04","modified_gmt":"2023-04-04T10:07:04","slug":"determina-o-conjunto-solucao-das-equacoes-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24804","title":{"rendered":"Determina o conjunto-solu\u00e7\u00e3o das equa\u00e7\u00f5es"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24804' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24804' class='GTTabs_curr'><a  id=\"24804_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24804' ><a  id=\"24804_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_24804'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determina o conjunto-solu\u00e7\u00e3o das seguintes equa\u00e7\u00f5es.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 160px;\">\n<tbody>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">a)<\/td>\n<td style=\"text-align: left; width: 96.875%; height: 20px;\">\\(x\\left( {x &#8211; 1} \\right) = 0\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">b)<\/td>\n<td style=\"text-align: left; width: 96.875%; height: 20px;\">\\(\\left( {a &#8211; 1} \\right)\\left( {a + 1} \\right) = 0\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">c)<\/td>\n<td style=\"text-align: left; width: 96.875%; height: 20px;\">\\({x^2} &#8211; 2x = 0\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">d)<\/td>\n<td style=\"text-align: left; width: 96.875%; height: 20px;\">\\(2{x^2} = 32\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">e)<\/td>\n<td style=\"text-align: left; width: 96.875%; height: 20px;\">\\({c^2} &#8211; 0,25 = 0\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">f)<\/td>\n<td style=\"text-align: left; width: 96.875%; height: 20px;\">\\({x^2} = 0,01\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">g)<\/td>\n<td style=\"text-align: left; width: 96.875%; height: 20px;\">\\({y^3} &#8211; 4y = 0\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 3.125%; height: 20px;\">h)<\/td>\n<td style=\"text-align: left; width: 96.875%; height: 20px;\">\\({x^2} &#8211; 256 = 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_24804' onClick='GTTabs_show(1,24804)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24804'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>O conjunto-solu\u00e7\u00e3o das equa\u00e7\u00f5es est\u00e1 apresentado abaixo.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 3.125%;\">a)<\/td>\n<td style=\"width: 48.4375%;\">\\[\\begin{array}{*{20}{l}}{x\\left( {x &#8211; 1} \\right) = 0}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{x &#8211; 1 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{x = 1}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"text-align: left; width: 48.4375%;\">\\[S = \\left\\{ {0,\\;1} \\right\\}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">b)<\/td>\n<td style=\"width: 48.4375%;\">\\[\\begin{array}{*{20}{l}}{\\left( {a &#8211; 1} \\right)\\left( {a + 1} \\right) = 0}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{a &#8211; 1 = 0}&amp; \\vee &amp;{a + 1 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{a = 1}&amp; \\vee &amp;{a = &#8211; 1}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"text-align: left; width: 48.4375%;\">\\[S = \\left\\{ { &#8211; 1,\\;1} \\right\\}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">c)<\/td>\n<td style=\"width: 48.4375%;\">\\[\\begin{array}{*{20}{l}}{{x^2} &#8211; 2x = 0}&amp; \\Leftrightarrow &amp;{x\\left( {x &#8211; 2} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{x &#8211; 2 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{x = 2}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"text-align: left; width: 48.4375%;\">\\[S = \\left\\{ {0,\\;2} \\right\\}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">d)<\/td>\n<td style=\"width: 48.4375%;\">\\[\\begin{array}{*{20}{l}}{2{x^2} = 32}&amp; \\Leftrightarrow &amp;{{x^2} = 16}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 4}&amp; \\vee &amp;{x = 4}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"text-align: left; width: 48.4375%;\">\\[S = \\left\\{ { &#8211; 4,\\;4} \\right\\}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">e)<\/td>\n<td style=\"width: 48.4375%;\">\\[\\begin{array}{*{20}{l}}{{c^2} &#8211; 0,25 = 0}&amp; \\Leftrightarrow &amp;{{c^2} = 0,25}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 0,5}&amp; \\vee &amp;{x = 0,5}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"text-align: left; width: 48.4375%;\">\\[S = \\left\\{ { &#8211; 0,5;\\;0,5} \\right\\}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">f)<\/td>\n<td style=\"width: 48.4375%;\">\\[\\begin{array}{*{20}{l}}{{x^2} = 0,01}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 0,1}&amp; \\vee &amp;{x = 0,1}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"text-align: left; width: 48.4375%;\">\\[S = \\left\\{ { &#8211; 0,1;\\;0,1} \\right\\}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">g)<\/td>\n<td style=\"width: 48.4375%;\">\\[\\begin{array}{*{20}{l}}{{y^3} &#8211; 4y = 0}&amp; \\Leftrightarrow &amp;{y\\left( {{y^2} &#8211; 4} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{y = 0}&amp; \\vee &amp;{{y^2} &#8211; 4 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{y = 0}&amp; \\vee &amp;{{y^2} = 4}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}{y = 0}&amp; \\vee &amp;{y = &#8211; 2}&amp; \\vee &amp;{y = 2}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"text-align: left; width: 48.4375%;\">\\[S = \\left\\{ { &#8211; 2,\\;0,\\;2} \\right\\}\\]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.125%;\">h)<\/td>\n<td style=\"width: 48.4375%;\">\\[\\begin{array}{*{20}{l}}{{x^2} &#8211; 256 = 0}&amp; \\Leftrightarrow &amp;{{x^2} = 256}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; \\sqrt {256} }&amp; \\vee &amp;{x = \\sqrt {256} }\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 16}&amp; \\vee &amp;{x = 16}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"text-align: left; width: 48.4375%;\">\\[S = \\left\\{ { &#8211; 16,\\;16} \\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_24804' onClick='GTTabs_show(0,24804)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determina o conjunto-solu\u00e7\u00e3o das seguintes equa\u00e7\u00f5es. a) \\(x\\left( {x &#8211; 1} \\right) = 0\\) b) \\(\\left( {a &#8211; 1} \\right)\\left( {a + 1} \\right) = 0\\) c) \\({x^2} &#8211; 2x =&#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":[100,97,700],"tags":[424,706,198],"series":[],"class_list":["post-24804","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":117,"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\/24804","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=24804"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24804\/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=24804"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24804"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24804"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24804"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}