{"id":24786,"date":"2023-04-03T17:23:34","date_gmt":"2023-04-03T16:23:34","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24786"},"modified":"2023-04-03T17:53:52","modified_gmt":"2023-04-03T16:53:52","slug":"determina-o-conjunto-solucao-das-equacoes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24786","title":{"rendered":"Determina o conjunto-solu\u00e7\u00e3o das equa\u00e7\u00f5es"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24786' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24786' class='GTTabs_curr'><a  id=\"24786_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24786' ><a  id=\"24786_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_24786'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determina o conjunto-solu\u00e7\u00e3o de cada uma das equa\u00e7\u00f5es:<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 100px;\">\n<tbody>\n<tr style=\"height: 20px;\">\n<td style=\"height: 20px; width: 3.38541%;\">a)<\/td>\n<td style=\"height: 20px; text-align: left; width: 96.4844%;\">\\({x^2} &#8211; 16 = 0\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"height: 20px; width: 3.38541%;\">b)<\/td>\n<td style=\"height: 20px; text-align: left; width: 96.4844%;\">\\(x\\left( {{x^2} &#8211; 25} \\right) = 0\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"height: 20px; width: 3.38541%;\">c)<\/td>\n<td style=\"height: 20px; text-align: left; width: 96.4844%;\">\\(8{x^3} &#8211; 2x = 0\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"height: 20px; width: 3.38541%;\">d)<\/td>\n<td style=\"height: 20px; text-align: left; width: 96.4844%;\">\\({x^2} &#8211; 36 = 0\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"height: 20px; width: 3.38541%;\">e)<\/td>\n<td style=\"height: 20px; text-align: left; width: 96.4844%;\">\\({\\left( {x + 1} \\right)^2} &#8211; \\left( {x + 1} \\right) = 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_24786' onClick='GTTabs_show(1,24786)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24786'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>O conjunto-solu\u00e7\u00e3o de cada uma das equa\u00e7\u00f5es est\u00e1 apresentado abaixo.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 100px;\">\n<tbody>\n<tr style=\"height: 20px;\">\n<td style=\"height: 20px; width: 3.38541%;\">a)<\/td>\n<td style=\"height: 20px; text-align: left; width: 48.2422%;\">\\[\\begin{array}{*{20}{l}}{{x^2} &#8211; 16 = 0}&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: 48.2422%;\">\\[S = \\left\\{ { &#8211; 4,\\;4} \\right\\}\\]<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"height: 20px; width: 3.38541%;\">b)<\/td>\n<td style=\"height: 20px; text-align: left; width: 48.2422%;\">\\[\\begin{array}{*{20}{l}}{x\\left( {{x^2} &#8211; 25} \\right) = 0}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{{x^2} &#8211; 25 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{{x^2} = 25}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}{x = 0}&amp; \\vee &amp;{x = &#8211; 5}&amp; \\vee &amp;{x = 5}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"text-align: left; width: 48.2422%;\">\\[S = \\left\\{ { &#8211; 5,\\;0,\\;5} \\right\\}\\]<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"height: 20px; width: 3.38541%;\">c)<\/td>\n<td style=\"height: 20px; text-align: left; width: 48.2422%;\">\\[\\begin{array}{*{20}{l}}{8{x^3} &#8211; 2x = 0}&amp; \\Leftrightarrow &amp;{2x\\left( {4{x^2} &#8211; 1} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{2x = 0}&amp; \\vee &amp;{4{x^2} &#8211; 1 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{{x^2} = \\frac{1}{4}}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}{x = 0}&amp; \\vee &amp;{x = &#8211; \\frac{1}{2}}&amp; \\vee &amp;{x = \\frac{1}{2}}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"text-align: left; width: 48.2422%;\">\\[S = \\left\\{ { &#8211; \\frac{1}{2},\\;0,\\;\\frac{1}{2}} \\right\\}\\]<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"height: 20px; width: 3.38541%;\">d)<\/td>\n<td style=\"height: 20px; text-align: left; width: 48.2422%;\">\\[\\begin{array}{*{20}{l}}{{x^2} &#8211; 36 = 0}&amp; \\Leftrightarrow &amp;{{x^2} = 36}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 6}&amp; \\vee &amp;{x = 6}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"text-align: left; width: 48.2422%;\">\\[S = \\left\\{ { &#8211; 6,\\;6} \\right\\}\\]<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"height: 20px; width: 3.38541%;\">e)<\/td>\n<td style=\"height: 20px; text-align: left; width: 48.2422%;\">\\[\\begin{array}{*{20}{l}}{{{\\left( {x + 1} \\right)}^2} &#8211; \\left( {x + 1} \\right) = 0}&amp; \\Leftrightarrow &amp;{\\left( {x + 1} \\right)\\left[ {\\left( {x + 1} \\right) &#8211; 1} \\right] = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\left( {x + 1} \\right)x = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x + 1 = 0}&amp; \\vee &amp;{x = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 1}&amp; \\vee &amp;{x = 0}\\end{array}}\\end{array}\\]<\/td>\n<td style=\"text-align: left; width: 48.2422%;\">\\[S = \\left\\{ { &#8211; 1,\\;0} \\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_24786' onClick='GTTabs_show(0,24786)'>&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 de cada uma das equa\u00e7\u00f5es: a) \\({x^2} &#8211; 16 = 0\\) b) \\(x\\left( {{x^2} &#8211; 25} \\right) = 0\\) c) \\(8{x^3} &#8211; 2x = 0\\) d) \\({x^2} &#8211;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19179,"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-24786","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":83,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat70.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24786","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=24786"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24786\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24786"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24786"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24786"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}