{"id":24824,"date":"2023-04-04T15:00:49","date_gmt":"2023-04-04T14:00:49","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24824"},"modified":"2023-04-04T17:08:29","modified_gmt":"2023-04-04T16:08:29","slug":"escolhe-dois-numeros-quaisquer","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24824","title":{"rendered":"Escolhe dois n\u00fameros inteiros quaisquer"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24824' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24824' class='GTTabs_curr'><a  id=\"24824_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24824' ><a  id=\"24824_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_24824'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Escolhe dois n\u00fameros inteiros quaisquer.<\/p>\n<ol>\n<li>Calcula o quadrado da soma.<\/li>\n<li>Calcula o quadrado da diferen\u00e7a.<\/li>\n<li>Subtrai os n\u00fameros obtidos em 1. e 2.<\/li>\n<li>Repete o que fizeste nas al\u00edneas 1., 2. e 3. utilizando outros n\u00fameros inteiros.<br \/>O que observas? Procura generalizar o que descobriste.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24824' onClick='GTTabs_show(1,24824)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24824'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Escolhe dois n\u00fameros inteiros quaisquer.<\/p>\n<\/blockquote>\n<ol>\n<li>\n<blockquote>Calcula o quadrado da soma.<\/blockquote>\n<\/li>\n<li>\n<blockquote>Calcula o quadrado da diferen\u00e7a.<\/blockquote>\n<\/li>\n<li>\n<blockquote>Subtrai os n\u00fameros obtidos em 1. e 2.<\/blockquote>\n<\/li>\n<li>\n<blockquote>Repete o que fizeste nas al\u00edneas 1., 2. e 3. utilizando outros n\u00fameros inteiros.<br \/>O que observas? Procura generalizar o que descobriste.<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>Consideremos os n\u00fameros 5 e 8.<br \/>Ora, o quadrado da sua soma \u00e9 \\({\\left( {5 + 8} \\right)^2} = {13^2} = 169\\).<\/li>\n<li>O quadrado da sua diferen\u00e7a \u00e9 \\({\\left( {8 &#8211; 5} \\right)^2} = {3^2} = 9\\).<\/li>\n<li>A diferen\u00e7a entre o quadrado da soma e o quadrado da diferen\u00e7a desses n\u00fameros \u00e9 \\(169 &#8211; 9 = 160\\).<\/li>\n<li>Utilizando outros n\u00fameros e generalizando:<\/li>\n<\/ol>\n<table style=\"border-collapse: collapse; width: 100%; height: 162px;\">\n<tbody>\n<tr style=\"height: 62px;\">\n<td style=\"width: 20%; height: 62px;\">\\(a\\)<\/td>\n<td style=\"width: 20%; height: 62px;\">\\(b\\)<\/td>\n<td style=\"width: 20%; height: 62px;\">\\({\\left( {a + b} \\right)^2}\\)<\/td>\n<td style=\"width: 20%; height: 62px;\">\\({\\left( {a &#8211; b} \\right)^2}\\)<\/td>\n<td style=\"width: 20%; height: 62px;\">\\({\\left( {a + b} \\right)^2} &#8211; {\\left( {a &#8211; b} \\right)^2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 20%; height: 20px;\">\\(5\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\( &#8211; 3\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\(4\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\(64\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\( &#8211; 60\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 20%; height: 20px;\">\\( &#8211; 13\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\( &#8211; 4\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\(289\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\(81\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\(208\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 20%; height: 20px;\">\\(5\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\(20\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\(625\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\(225\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\(400\\)<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 20%; height: 20px;\">&#8230;<\/td>\n<td style=\"width: 20%; height: 20px;\">&#8230;<\/td>\n<td style=\"width: 20%; height: 20px;\">&#8230;<\/td>\n<td style=\"width: 20%; height: 20px;\">&#8230;<\/td>\n<td style=\"width: 20%; height: 20px;\">&#8230;<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"width: 20%; height: 20px;\">\\(a\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\(b\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\({a^2} + 2ab + {b^2}\\)<\/td>\n<td style=\"width: 20%; height: 20px;\">\\({a^2} &#8211; 2ab + {b^2}\\)<\/td>\n<td style=\"width: 20%; height: 20px;\"><strong>\\(4ab\\)<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24824' onClick='GTTabs_show(0,24824)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Escolhe dois n\u00fameros inteiros quaisquer. Calcula o quadrado da soma. Calcula o quadrado da diferen\u00e7a. Subtrai os n\u00fameros obtidos em 1. e 2. Repete o que fizeste nas al\u00edneas 1., 2.&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19172,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,196,705],"series":[],"class_list":["post-24824","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-casos-notaveis","tag-polinomios"],"views":83,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat63.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24824","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=24824"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24824\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19172"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24824"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24824"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24824"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24824"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}