{"id":6775,"date":"2011-04-14T00:09:07","date_gmt":"2011-04-13T23:09:07","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6775"},"modified":"2022-01-18T02:20:53","modified_gmt":"2022-01-18T02:20:53","slug":"verifica-se-o-numero-indicado-e-solucao-da-equacao","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6775","title":{"rendered":"Verifica se o n\u00famero indicado \u00e9 solu\u00e7\u00e3o da equa\u00e7\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_6775' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6775' class='GTTabs_curr'><a  id=\"6775_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6775' ><a  id=\"6775_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_6775'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/01.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"12280\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=12280\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/01.png\" data-orig-size=\"460,460\" 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=\"01\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/01.png\" class=\"alignright wp-image-12280\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/01-300x300.png\" alt=\"01\" width=\"240\" height=\"240\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/01-300x300.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/01-150x150.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/01-160x160.png 160w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/01.png 460w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Verifica, sem resolveres as equa\u00e7\u00f5es, se o n\u00famero indicado entre par\u00eanteses \u00e9 ou n\u00e3o solu\u00e7\u00e3o da equa\u00e7\u00e3o:<\/p>\n<ol>\n<li>$\\frac{a-2}{5}+\\frac{a+3}{2}=\\frac{1}{10}$, $(0)$;<\/li>\n<li>$\\frac{3(x-1)}{2}-\\frac{2(x-1)}{3}=0$, $(1)$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6775' onClick='GTTabs_show(1,6775)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6775'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Substituindo a por $0$, vem:<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\n\\frac{0-2}{5}+\\frac{0+3}{2}=\\frac{1}{10} &amp; \\Leftrightarrow\u00a0 &amp; -\\frac{2}{\\underset{(2)}{\\mathop{5}}\\,}+\\frac{3}{\\underset{(5)}{\\mathop{2}}\\,}=\\frac{1}{10}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; -\\frac{4}{10}+\\frac{15}{10}=\\frac{1}{10}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{11}{10}=\\frac{1}{10}\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\nComo a proposi\u00e7\u00e3o obtida \u00e9 falsa, $0$ n\u00e3o \u00e9 solu\u00e7\u00e3o da equa\u00e7\u00e3o.<br \/>\n\u00ad<\/li>\n<li>Substituindo x por $1$, vem:<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\n\\frac{3(1-1)}{2}-\\frac{2(1-1)}{3}=0 &amp; \\Leftrightarrow\u00a0 &amp; 0-0=0\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 0=0\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\nComo a proposi\u00e7\u00e3o obtida \u00e9 verdadeira,\u00a0\u00a0$1$ \u00e9 solu\u00e7\u00e3o da equa\u00e7\u00e3o.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6775' onClick='GTTabs_show(0,6775)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Verifica, sem resolveres as equa\u00e7\u00f5es, se o n\u00famero indicado entre par\u00eanteses \u00e9 ou n\u00e3o solu\u00e7\u00e3o da equa\u00e7\u00e3o: $\\frac{a-2}{5}+\\frac{a+3}{2}=\\frac{1}{10}$, $(0)$; $\\frac{3(x-1)}{2}-\\frac{2(x-1)}{3}=0$, $(1)$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20584,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,159],"tags":[425],"series":[],"class_list":["post-6775","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-do-1--grau","tag-equacoes"],"views":2619,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/04\/8V2Pag057-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6775","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=6775"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6775\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20584"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6775"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6775"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6775"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6775"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}