{"id":24585,"date":"2023-03-10T14:27:42","date_gmt":"2023-03-10T14:27:42","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=24585"},"modified":"2023-03-10T16:06:40","modified_gmt":"2023-03-10T16:06:40","slug":"a-descoberta-dos-numeros","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=24585","title":{"rendered":"\u00c0 descoberta dos n\u00fameros"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_24585' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_24585' class='GTTabs_curr'><a  id=\"24585_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_24585' ><a  id=\"24585_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_24585'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24587\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24587\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-1.png\" data-orig-size=\"369,900\" 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=\"8Pag140-T9-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-1.png\" class=\"alignright wp-image-24587\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-1-123x300.png\" alt=\"\" width=\"240\" height=\"585\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-1-123x300.png 123w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-1.png 369w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>L\u00ea o que diz o Miguel.<br \/>O Miguel pode ter pensado nos n\u00fameros \\(3\\) e \\( &#8211; 2\\)? Porqu\u00ea?<\/li>\n<li>Escreve dois n\u00fameros em que o Miguel possa ter pensado.<\/li>\n<li>Escreve agora mais quatro pares de n\u00fameros nessa condi\u00e7\u00f5es.<\/li>\n<li>O que podes dizer sobre os n\u00fameros em que o Miguel pensou?<br \/>Explica a tua resposta.<\/li>\n<li>Em que n\u00famero pensou a Catarina? Explica a tua resposta.<\/li>\n<li>O Jos\u00e9 e a Marta tamb\u00e9m quiseram entrar no jogo \u00c0 descoberta dos n\u00fameros&#8230;<\/li>\n<\/ol>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24588\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24588\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2.png\" data-orig-size=\"959,662\" 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=\"8Pag140-T9-2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2.png\" class=\"alignnone wp-image-24588\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2-300x207.png\" alt=\"\" width=\"580\" height=\"400\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2-300x207.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2-768x530.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2.png 959w\" sizes=\"auto, (max-width: 580px) 100vw, 580px\" \/><\/a><\/p>\n<p>\u00a0<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Em que n\u00fameros pensou o Jos\u00e9?<br \/>Explica a tua resposta.<\/li>\n<li>A que n\u00famero se refere a Marta?<br \/>Explica a tua resposta.<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_24585' onClick='GTTabs_show(1,24585)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_24585'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24587\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24587\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-1.png\" data-orig-size=\"369,900\" 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=\"8Pag140-T9-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-1.png\" class=\"alignright wp-image-24587\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-1-123x300.png\" alt=\"\" width=\"240\" height=\"585\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-1-123x300.png 123w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-1.png 369w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>O Miguel n\u00e3o pode ter pensado nos n\u00fameros \\(3\\) e \\( &#8211; 2\\), pois o produto desses n\u00fameros n\u00e3o \u00e9 nulo.<\/li>\n<li>O Miguel pode ter pensado nos n\u00fameros \\(0\\) e \\( &#8211; 2\\).<\/li>\n<li>Mais quatro pares de n\u00fameros nessas condi\u00e7\u00f5es: \\(4\\) e \\(0\\); \\({ &#8211; 4}\\) e \\(0\\); \\(0\\) e \\({ &#8211; \\pi }\\); e \\(0\\) e \\({\\sqrt 3 }\\).<\/li>\n<li>Pelo menos um dos n\u00fameros em que o Miguel pensou ter\u00e1 de ser zero, pois um produto de dois n\u00fameros ser\u00e1 nulo apenas se, pelo menos, um deles for nulo.<\/li>\n<li>Se designarmos o n\u00famero em que a Catarina pensou por \\(x\\), podemos equacionar a quest\u00e3o desta forma: \\(\\left( {x &#8211; 2} \\right)\\left( {x + 3} \\right) = 0\\). Assim, podemos concluir que a Catarina ter\u00e1 pensado no n\u00famero \\(2\\) ou no n\u00famero \\( &#8211; 3\\).<\/li>\n<li>O Jos\u00e9 e a Marta tamb\u00e9m quiseram entrar no jogo \u00c0 descoberta dos n\u00fameros&#8230;<\/li>\n<\/ol>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"24588\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=24588\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2.png\" data-orig-size=\"959,662\" 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=\"8Pag140-T9-2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2.png\" class=\"alignnone wp-image-24588\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2-300x207.png\" alt=\"\" width=\"580\" height=\"400\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2-300x207.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2-768x530.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2.png 959w\" sizes=\"auto, (max-width: 580px) 100vw, 580px\" \/><\/a><\/p>\n<p>\u00a0<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Designado por \\(n\\) o n\u00famero mais pequeno em que o Jos\u00e9 pensou, podemos equacionar o problema como segue: \\(n\\left( {n + 6} \\right) = 2n\\).<br \/>Resolvendo a equa\u00e7\u00e3o, podemos concluir que o Jos\u00e9 pensou em \\(0\\) e em \\(6\\), ou em \\( &#8211; 4\\) e em \\(2\\):<br \/>\\[\\begin{array}{*{20}{l}}{n\\left( {n + 6} \\right) = 2n}&amp; \\Leftrightarrow &amp;{{n^2} + 6n &#8211; 2n = 0}\\\\{}&amp; \\Leftrightarrow &amp;{{n^2} + 4n = 0}\\\\{}&amp; \\Leftrightarrow &amp;{n\\left( {n + 4} \\right) = 0}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{n = 0}&amp; \\vee &amp;{n = &#8211; 4}\\end{array}}\\end{array}\\]<\/li>\n<li>Designado por \\(m\\) o n\u00famero referido pela Marta, podemos equacionar o problema como segue: \\(3{m^2} &#8211; 75 = 0\\).<br \/>Resolvendo a equa\u00e7\u00e3o, podemos concluir que a Mariana se referiu ao n\u00famero \\(5\\) ou ao n\u00famero \\( &#8211; 5\\):<br \/>\\[\\begin{array}{*{20}{l}}{3{m^2} &#8211; 75 = 0}&amp; \\Leftrightarrow &amp;{3{m^2} = 75}\\\\{}&amp; \\Leftrightarrow &amp;{{m^2} = 25}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{m = 5}&amp; \\vee &amp;{m = &#8211; 5}\\end{array}}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_24585' onClick='GTTabs_show(0,24585)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado L\u00ea o que diz o Miguel.O Miguel pode ter pensado nos n\u00fameros \\(3\\) e \\( &#8211; 2\\)? Porqu\u00ea? Escreve dois n\u00fameros em que o Miguel possa ter pensado. Escreve agora mais&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":24589,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,700],"tags":[424,197,706,705],"series":[],"class_list":["post-24585","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-decomposicao-em-factores","tag-equacao-incompleta-do-2-o-grau","tag-polinomios"],"views":129,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/03\/8Pag140-T9-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24585","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=24585"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/24585\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/24589"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24585"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24585"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24585"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=24585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}