{"id":11855,"date":"2014-04-30T15:14:26","date_gmt":"2014-04-30T14:14:26","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11855"},"modified":"2021-12-26T13:31:36","modified_gmt":"2021-12-26T13:31:36","slug":"resolva-em-mathbbr-as-seguintes-equacoes-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11855","title":{"rendered":"Resolva, em $\\mathbb{R}$, as seguintes equa\u00e7\u00f5es"},"content":{"rendered":"<p><ul id='GTTabs_ul_11855' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11855' class='GTTabs_curr'><a  id=\"11855_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11855' ><a  id=\"11855_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_11855'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Resolva, em $\\mathbb{R}$, as seguintes equa\u00e7\u00f5es:<\/p>\n<ol>\n<li>${x^4} = 625$<\/li>\n<li>${x^3} =\u00a0 &#8211; 125$<\/li>\n<li>${x^4} + 81 = 0$<\/li>\n<li>${x^3} &#8211; 343 = 0$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11855' onClick='GTTabs_show(1,11855)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11855'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Tem-se sucessivamente:<br \/>\n\\[\\begin{array}{*{20}{l}}<br \/>\n{{x^4} = 625}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{x =\u00a0 &#8211; \\sqrt[4]{{625}}}&amp; \\vee &amp;{x = \\sqrt[4]{{625}}}<br \/>\n\\end{array}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{x =\u00a0 &#8211; \\sqrt[4]{{{5^4}}}}&amp; \\vee &amp;{x = \\sqrt[4]{{{5^4}}}}<br \/>\n\\end{array}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{x =\u00a0 &#8211; 5}&amp; \\vee &amp;{x = 5}<br \/>\n\\end{array}}<br \/>\n\\end{array}\\]<\/li>\n<li>Tem-se sucessivamente:<br \/>\n\\[\\begin{array}{*{20}{l}}<br \/>\n{{x^3} =\u00a0 &#8211; 125}&amp; \\Leftrightarrow &amp;{x = \\sqrt[3]{{ &#8211; 125}}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{x =\u00a0 &#8211; \\sqrt[3]{{{5^3}}}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{x =\u00a0 &#8211; 5}<br \/>\n\\end{array}\\]<\/li>\n<li>Tem-se sucessivamente:<br \/>\n\\[\\begin{array}{*{20}{l}}<br \/>\n{{x^4} + 81 = 0}&amp; \\Leftrightarrow &amp;{{x^4} =\u00a0 &#8211; 81} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{x \\in \\emptyset }<br \/>\n\\end{array}\\]<\/li>\n<li>Tem-se sucessivamente:<br \/>\n\\[\\begin{array}{*{20}{l}}<br \/>\n{{x^3} &#8211; 343 = 0}&amp; \\Leftrightarrow &amp;{{x^3} = 343} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{x = \\sqrt[3]{{{7^3}}}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{x = 7}<br \/>\n\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11855' onClick='GTTabs_show(0,11855)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Resolva, em $\\mathbb{R}$, as seguintes equa\u00e7\u00f5es: ${x^4} = 625$ ${x^3} =\u00a0 &#8211; 125$ ${x^4} + 81 = 0$ ${x^3} &#8211; 343 = 0$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14113,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,157],"tags":[422,370],"series":[],"class_list":["post-11855","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-funcoes-com-radicais","tag-11-o-ano","tag-funcao-potencia"],"views":1825,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat55.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11855","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=11855"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11855\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14113"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11855"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11855"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11855"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11855"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}