{"id":14571,"date":"2018-04-15T22:05:20","date_gmt":"2018-04-15T21:05:20","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14571"},"modified":"2022-01-07T22:45:48","modified_gmt":"2022-01-07T22:45:48","slug":"a-idade-da-joana","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14571","title":{"rendered":"A idade da Joana"},"content":{"rendered":"<p><ul id='GTTabs_ul_14571' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14571' class='GTTabs_curr'><a  id=\"14571_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14571' ><a  id=\"14571_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_14571'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-9a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14572\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14572\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-9a.png\" data-orig-size=\"520,245\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Rapariga\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-9a.png\" class=\"alignright size-medium wp-image-14572\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-9a-300x141.png\" alt=\"\" width=\"300\" height=\"141\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-9a-300x141.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-9a-720x340.png 720w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-9a.png 520w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>O produto da idade que a Joana ter\u00e1 daqui a tr\u00eas anos pela sua idade h\u00e1 dois anos atr\u00e1s \u00e9 84.<\/p>\n<p>Qual \u00e9 a idade da Joana?<br \/>\nExplica a tua resposta.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14571' onClick='GTTabs_show(1,14571)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14571'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Seja <em>x<\/em> a idade atual da Joana, em anos (\\(x \\ge 2\\)).<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\begin{array}{*{20}{c}}{\\left( {x + 3} \\right)\\left( {x &#8211; 2} \\right) = 84}&amp; \\wedge &amp;{x \\ge 2}\\end{array}}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{{x^2} &#8211; 2x + 3x &#8211; 6 = 84}&amp; \\wedge &amp;{x \\ge 2}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{{x^2} + x &#8211; 90 = 0}&amp; \\wedge &amp;{x \\ge 2}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{x = \\frac{{ &#8211; 1 \\mp \\sqrt {1 + 360} }}{2}}&amp; \\wedge &amp;{x \\ge 2}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{\\left( {\\begin{array}{*{20}{c}}{x = \\frac{{ &#8211; 1 &#8211; 19}}{2}}&amp; \\vee &amp;{x = \\frac{{ &#8211; 1 + 19}}{2}}\\end{array}} \\right)}&amp; \\wedge &amp;{x \\ge 2}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{x = 9}\\end{array}\\]<\/p>\n<p>Portanto, a Joana tem 9 anos de idade.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14571' onClick='GTTabs_show(0,14571)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O produto da idade que a Joana ter\u00e1 daqui a tr\u00eas anos pela sua idade h\u00e1 dois anos atr\u00e1s \u00e9 84. Qual \u00e9 a idade da Joana? Explica a tua resposta.&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14572,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,306,304],"series":[],"class_list":["post-14571","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-equacoes-do-2-o-grau","tag-9-o-ano","tag-equacao-do-2-o-grau","tag-formula-resolvente"],"views":3089,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-9a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14571","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=14571"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14571\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14572"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14571"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14571"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14571"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14571"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}