\nEnunciado<\/b><\/span><\/p>\n
Desenvolve e simplifica cada uma das seguintes express\u00f5es:<\/p>\n
\n
$15x-{{(x+7)}^{2}}$<\/li>\n
$x(x-1)-{{(x-2)}^{2}}$<\/li>\n
$(x+2)(x-3)+{{(x+1)}^{2}}$<\/li>\n
${{(x+\\frac{1}{2})}^{2}}-{{(x-\\frac{1}{2})}^{2}}-\\frac{3}{4}(x-1)(x+1)$<\/li>\n<\/ol>\n
Resolu\u00e7\u00e3o >><\/a><\/span><\/div><\/div>\n\n
\nResolu\u00e7\u00e3o<\/b><\/span><\/p>\n
\n
Ora,
\n\\[\\begin{array}{*{35}{l}}
\n15x-{{(x+7)}^{2}} & = & 15x-({{x}^{2}}+14x+49)\u00a0 \\\\
\n{} & = & 15x-{{x}^{2}}-14x-49\u00a0 \\\\
\n{} & = & -{{x}^{2}}+x-49\u00a0 \\\\
\n\\end{array}\\]<\/li>\n
Ora,
\n\\[\\begin{array}{*{35}{l}}
\nx(x-1)-{{(x-2)}^{2}} & = & {{x}^{2}}-x-({{x}^{2}}-4x+4)\u00a0 \\\\
\n{} & = & {{x}^{2}}-x-{{x}^{2}}+4x-4)\u00a0 \\\\
\n{} & = & 3x-4\u00a0 \\\\
\n\\end{array}\\]<\/li>\n
Ora,
\n\\[\\begin{array}{*{35}{l}}
\n(x+2)(x-3)+{{(x+1)}^{2}} & = & ({{x}^{2}}-3x+2x-6)+({{x}^{2}}+2x+1)\u00a0 \\\\
\n{} & = & {{x}^{2}}-3x+2x-6+{{x}^{2}}+2x+1\u00a0 \\\\
\n{} & = & 2{{x}^{2}}+x-5\u00a0 \\\\
\n\\end{array}\\]<\/li>\n
Ora,
\n\\[\\begin{array}{*{35}{l}}
\n{{(x+\\frac{1}{2})}^{2}}-{{(x-\\frac{1}{2})}^{2}}-\\frac{3}{4}(x-1)(x+1) & = & ({{x}^{2}}+x+\\frac{1}{4})-({{x}^{2}}-x+\\frac{1}{4})-\\frac{3}{4}({{x}^{2}}-1)\u00a0 \\\\
\n{} & = & {{x}^{2}}+x+\\frac{1}{4}-{{x}^{2}}+x-\\frac{1}{4}-\\frac{3}{4}{{x}^{2}}+\\frac{3}{4}\u00a0 \\\\
\n{} & = & -\\frac{3}{4}{{x}^{2}}+2x+\\frac{3}{4}\u00a0 \\\\
\n\\end{array}\\]<\/p>\n
Alternativa<\/strong>:
\n\\[\\begin{array}{*{35}{l}}
\n{{(x+\\frac{1}{2})}^{2}}-{{(x-\\frac{1}{2})}^{2}}-\\frac{3}{4}(x-1)(x+1) & = & \\left[ (x+\\frac{1}{2})+(x-\\frac{1}{2}) \\right]\\times \\left[ (x+\\frac{1}{2})-(x-\\frac{1}{2}) \\right]-\\frac{3}{4}({{x}^{2}}-1)\\,\\,\\,\\,\\text{(Porqu }\\!\\!\\hat{\\mathrm{e}}\\!\\!\\text{ ?)}\u00a0 \\\\
\n{} & = & 2x\\times 1-\\frac{3}{4}{{x}^{2}}+\\frac{3}{4}\u00a0 \\\\
\n{} & = & -\\frac{3}{4}{{x}^{2}}+2x+\\frac{3}{4}\u00a0 \\\\
\n\\end{array}\\]<\/p>\n<\/li>\n<\/ol>\n
<< Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"
Enunciado Resolu\u00e7\u00e3o Enunciado Desenvolve e simplifica cada uma das seguintes express\u00f5es: $15x-{{(x+7)}^{2}}$ $x(x-1)-{{(x-2)}^{2}}$ $(x+2)(x-3)+{{(x+1)}^{2}}$ ${{(x+\\frac{1}{2})}^{2}}-{{(x-\\frac{1}{2})}^{2}}-\\frac{3}{4}(x-1)(x+1)$ Resolu\u00e7\u00e3o >> Resolu\u00e7\u00e3o << Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19176,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,193],"tags":[196],"series":[],"class_list":["post-6896","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-de-grau-superior-ao-1-","tag-casos-notaveis"],"views":2883,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat67.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6896","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=6896"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6896\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19176"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6896"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6896"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6896"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6896"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}