{"id":24619,"date":"2023-03-12T14:31:16","date_gmt":"2023-03-12T14:31:16","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24619"},"modified":"2023-03-12T17:27:07","modified_gmt":"2023-03-12T17:27:07","slug":"resolve-as-equacoes-5","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24619","title":{"rendered":"Resolve as equa\u00e7\u00f5es"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24619' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24619' class='GTTabs_curr'><a  id=\"24619_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24619' ><a  id=\"24619_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_24619'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Resolve as equa\u00e7\u00f5es, utilizando a lei do anulamento do produto.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 3.64583%;\">a)<\/td>\n<td style=\"text-align: left; width: 96.3542%;\">\\(x\\left( {x + 2} \\right) = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.64583%;\">b)<\/td>\n<td style=\"text-align: left; width: 96.3542%;\">\\(\\left( {2x + 1} \\right)\\left( {x &#8211; \\frac{1}{3}} \\right) = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.64583%;\">c)<\/td>\n<td style=\"text-align: left; width: 96.3542%;\">\\({x^2} + 3x = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.64583%;\">d)<\/td>\n<td style=\"text-align: left; width: 96.3542%;\">\\(3{z^2} &#8211; 12z = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.64583%;\">e)<\/td>\n<td style=\"text-align: left; width: 96.3542%;\">\\(\\left( {x &#8211; 3} \\right)\\left( {2 + 7x} \\right) = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.64583%;\">f)<\/td>\n<td style=\"text-align: left; width: 96.3542%;\">\\(x\\left( {x + 1} \\right) + 2\\left( {x + 1} \\right) = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.64583%;\">g)<\/td>\n<td style=\"text-align: left; width: 96.3542%;\">\\( &#8211; x\\left( {x + 4} \\right) = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.64583%;\">h)<\/td>\n<td style=\"text-align: left; width: 96.3542%;\">\\(\\left( {x + 4} \\right)x &#8211; 3\\left( {x + 4} \\right) = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.64583%;\">i)<\/td>\n<td style=\"text-align: left; width: 96.3542%;\">\\(3{x^2} &#8211; 12 = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.64583%;\">j)<\/td>\n<td style=\"text-align: left; width: 96.3542%;\">\\(16x + 2{x^2} = 0\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 3.64583%;\">k)<\/td>\n<td style=\"text-align: left; width: 96.3542%;\">\\(2{m^2} + 5m = 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_24619' onClick='GTTabs_show(1,24619)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24619'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>As equa\u00e7\u00f5es est\u00e3o resolvidas por utiliza\u00e7\u00e3o da lei do anulamento do produto.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 745px;\">\n<tbody>\n<tr style=\"height: 62px;\">\n<td style=\"width: 3.64583%; height: 62px; vertical-align: top;\">a)<\/td>\n<td style=\"text-align: left; width: 96.3542%; height: 62px;\">\\(\\begin{array}{*{20}{l}}{x\\left( {x + 2} \\right) = 0}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{x + 2 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{x = &#8211; 2}\\end{array}}\\end{array}\\)<\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"width: 3.64583%; height: 62px; vertical-align: top;\">b)<\/td>\n<td style=\"text-align: left; width: 96.3542%; height: 62px;\">\\(\\begin{array}{*{20}{l}}{\\left( {2x + 1} \\right)\\left( {x &#8211; \\frac{1}{3}} \\right) = 0}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{2x + 1 = 0}&amp; \\vee &amp;{x &#8211; \\frac{1}{3} = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; \\frac{1}{2}}&amp; \\vee &amp;{x = \\frac{1}{3}}\\end{array}}\\end{array}\\)<\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"width: 3.64583%; height: 62px; vertical-align: top;\">c)<\/td>\n<td style=\"text-align: left; width: 96.3542%; height: 62px;\">\\(\\begin{array}{*{20}{l}}{{x^2} + 3x = 0}&amp; \\Leftrightarrow &amp;{x\\left( {x + 3} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{x + 3 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{x = &#8211; 3}\\end{array}}\\end{array}\\)<\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"width: 3.64583%; height: 62px; vertical-align: top;\">d)<\/td>\n<td style=\"text-align: left; width: 96.3542%; height: 62px;\">\\(\\begin{array}{*{20}{l}}{3{z^2} &#8211; 12z = 0}&amp; \\Leftrightarrow &amp;{3z\\left( {z &#8211; 4} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{3z = 0}&amp; \\vee &amp;{z &#8211; 4 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{z = 0}&amp; \\vee &amp;{z = 4}\\end{array}}\\end{array}\\)<\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"width: 3.64583%; height: 62px; vertical-align: top;\">e)<\/td>\n<td style=\"text-align: left; width: 96.3542%; height: 62px;\">\\(\\begin{array}{*{20}{l}}{\\left( {x &#8211; 3} \\right)\\left( {2 + 7x} \\right) = 0}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x &#8211; 3 = 0}&amp; \\vee &amp;{2 + 7x = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 3}&amp; \\vee &amp;{x = &#8211; \\frac{2}{7}}\\end{array}}\\end{array}\\)<\/td>\n<\/tr>\n<tr style=\"height: 83px;\">\n<td style=\"width: 3.64583%; height: 83px; vertical-align: top;\">f)<\/td>\n<td style=\"text-align: left; width: 96.3542%; height: 83px;\">\\(\\begin{array}{*{20}{l}}{x\\left( {x + 1} \\right) + 2\\left( {x + 1} \\right) = 0}&amp; \\Leftrightarrow &amp;{\\left( {x + 1} \\right)\\left( {x + 2} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x + 1 = 0}&amp; \\vee &amp;{x + 2 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 1}&amp; \\vee &amp;{x = &#8211; 2}\\end{array}}\\end{array}\\)<\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"width: 3.64583%; height: 62px; vertical-align: top;\">g)<\/td>\n<td style=\"text-align: left; width: 96.3542%; height: 62px;\">\\(\\begin{array}{*{20}{l}}{ &#8211; x\\left( {x + 4} \\right) = 0}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{ &#8211; x = 0}&amp; \\vee &amp;{x + 4 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{x = &#8211; 4}\\end{array}}\\end{array}\\)<\/td>\n<\/tr>\n<tr style=\"height: 83px;\">\n<td style=\"width: 3.64583%; height: 83px; vertical-align: top;\">h)<\/td>\n<td style=\"text-align: left; width: 96.3542%; height: 83px;\">\\(\\begin{array}{*{20}{l}}{\\left( {x + 4} \\right)x &#8211; 3\\left( {x + 4} \\right) = 0}&amp; \\Leftrightarrow &amp;{\\left( {x + 4} \\right)\\left( {x &#8211; 3} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x + 4 = 0}&amp; \\vee &amp;{x &#8211; 3 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 4}&amp; \\vee &amp;{x = 3}\\end{array}}\\end{array}\\)<\/td>\n<\/tr>\n<tr style=\"height: 83px;\">\n<td style=\"width: 3.64583%; height: 83px; vertical-align: top;\">i)<\/td>\n<td style=\"text-align: left; width: 96.3542%; height: 83px;\">\\(\\begin{array}{*{20}{l}}{3{x^2} &#8211; 12 = 0}&amp; \\Leftrightarrow &amp;{3\\left( {{x^2} &#8211; 4} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{3\\left( {x + 2} \\right)\\left( {x &#8211; 2} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x + 2 = 0}&amp; \\vee &amp;{x &#8211; 2 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = &#8211; 2}&amp; \\vee &amp;{x = 2}\\end{array}}\\end{array}\\)<\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"width: 3.64583%; height: 62px; vertical-align: top;\">j)<\/td>\n<td style=\"text-align: left; width: 96.3542%; height: 62px;\">\\(\\begin{array}{*{20}{l}}{16x + 2{x^2} = 0}&amp; \\Leftrightarrow &amp;{2x\\left( {8 + x} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{2x = 0}&amp; \\vee &amp;{8 + x = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = 0}&amp; \\vee &amp;{x = &#8211; 8}\\end{array}}\\end{array}\\)<\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"width: 3.64583%; height: 62px; vertical-align: top;\">k)<\/td>\n<td style=\"text-align: left; width: 96.3542%; height: 62px;\">\\(\\begin{array}{*{20}{l}}{2{m^2} + 5m = 0}&amp; \\Leftrightarrow &amp;{m\\left( {2m + 5} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{m = 0}&amp; \\vee &amp;{2m + 5 = 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{m = 0}&amp; \\vee &amp;{m = &#8211; \\frac{5}{2}}\\end{array}}\\end{array}\\)<\/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_24619' onClick='GTTabs_show(0,24619)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolve as equa\u00e7\u00f5es, utilizando a lei do anulamento do produto. a) \\(x\\left( {x + 2} \\right) = 0\\) b) \\(\\left( {2x + 1} \\right)\\left( {x &#8211; \\frac{1}{3}} \\right) = 0\\) c)&#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":[424,706,198,705],"series":[],"class_list":["post-24619","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","tag-polinomios"],"views":142,"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\/24619","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=24619"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24619\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19189"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24619"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24619"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24619"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24619"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}