{"id":8604,"date":"2012-04-19T22:47:31","date_gmt":"2012-04-19T21:47:31","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8604"},"modified":"2022-01-16T11:33:59","modified_gmt":"2022-01-16T11:33:59","slug":"quantas-avelas-tem-o-kilo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8604","title":{"rendered":"Quantas avel\u00e3s tem o Kil\u00f3?"},"content":{"rendered":"<p><ul id='GTTabs_ul_8604' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8604' class='GTTabs_curr'><a  id=\"8604_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8604' ><a  id=\"8604_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_8604'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-8.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"8607\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=8607\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-8.jpg\" data-orig-size=\"520,311\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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;}\" data-image-title=\"Kili e Kil\u00f3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-8.jpg\" class=\"alignright  wp-image-8607\" title=\"Kili e Kil\u00f3\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-8.jpg\" alt=\"\" width=\"312\" height=\"187\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-8.jpg 520w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-8-300x179.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-8-150x89.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9pag69-8-400x239.jpg 400w\" sizes=\"auto, (max-width: 312px) 100vw, 312px\" \/><\/a>O Esquilo Kili diz ao Esquilo Kil\u00f3:<\/p>\n<p>&#8211; S\u00f3 tenho duas avel\u00e3s!<\/p>\n<p>E o Kil\u00f3 respondeu:<\/p>\n<p>&#8211; Metade do quadrado do n\u00famero das minhas avel\u00e3s \u00e9 igual ao seu qu\u00edntuplo. E tenho mais avel\u00e3s do que tu!<\/p>\n<p>Quantas avel\u00e3s tem o Kil\u00f3?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8604' onClick='GTTabs_show(1,8604)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8604'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>O Esquilo Kili diz ao Esquilo Kil\u00f3:<\/p>\n<p>&#8211; S\u00f3 tenho duas avel\u00e3s!<\/p>\n<p>E o Kil\u00f3 respondeu:<\/p>\n<p>&#8211; Metade do quadrado do n\u00famero das minhas avel\u00e3s \u00e9 igual ao seu qu\u00edntuplo. E tenho mais avel\u00e3s do que tu!<\/p>\n<p>Quantas avel\u00e3s tem o Kil\u00f3?<\/p>\n<\/blockquote>\n<p>\u00ad<\/p>\n<p>Seja $x$ o n\u00famero de avel\u00e3s que tem o Kil\u00f3.<\/p>\n<ul>\n<li>metade do quadrado do n\u00famero das avel\u00e3s do Kil\u00f3: $\\frac{{{x^2}}}{2}$<\/li>\n<li>qu\u00edntuplo do n\u00famero das avel\u00e3s do Kil\u00f3: $5x$<\/li>\n<\/ul>\n<p>$$\\begin{array}{*{20}{l}} \u00a0 {\\frac{{{x^2}}}{2} = 5x}&amp; \\Leftrightarrow &amp;{{x^2} &#8211; 10x = 0} \\\\ \u00a0 {}&amp; \\Leftrightarrow &amp;{x\\left( {x &#8211; 10} \\right) = 0} \\\\ \u00a0 {}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}} \u00a0 {x = 0}&amp; \\vee &amp;{x &#8211; 10 = 0} \\end{array}} \\\\ \u00a0 {}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}} \u00a0 {x = 0}&amp; \\vee &amp;{x = 10} \\end{array}} \\end{array}$$<\/p>\n<p>Como o Kil\u00f3 tem mais avel\u00e3s do que o Kili, ter\u00e1 de possuir mais de duas avel\u00e3s.<br \/>\nPortanto, o Kil\u00f3 tem 10 avel\u00e3s.<\/p>\n<p><strong>Nota<\/strong>: Ainda que a equa\u00e7\u00e3o possua duas solu\u00e7\u00f5es, uma delas n\u00e3o \u00e9 solu\u00e7\u00e3o do problema.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8604' onClick='GTTabs_show(0,8604)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Esquilo Kili diz ao Esquilo Kil\u00f3: &#8211; S\u00f3 tenho duas avel\u00e3s! E o Kil\u00f3 respondeu: &#8211; Metade do quadrado do n\u00famero das minhas avel\u00e3s \u00e9 igual ao seu qu\u00edntuplo. E&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20352,"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],"series":[],"class_list":["post-8604","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"],"views":2420,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/04\/9V2Pag069-8_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8604","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=8604"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8604\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20352"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8604"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8604"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8604"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8604"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}