{"id":224195,"date":"2025-02-19T21:18:39","date_gmt":"2025-02-20T00:18:39","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=224195"},"modified":"2025-02-19T21:18:39","modified_gmt":"2025-02-20T00:18:39","slug":"problemao-valor-de-expressao","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problemao-valor-de-expressao\/","title":{"rendered":".Problem\u00e3o: Valor de express\u00e3o"},"content":{"rendered":"

\n

\n

Problema
\n (Indicado a partir do 8\u00ba ano do E. F.)<\/span><\/p>\n

\nConsidere um n\u00famero [tex]a[\/tex], tal que [tex]a+\\dfrac{2}{a}=2[\/tex]. Determine o valor de [tex]a^3+\\dfrac{8}{a^3}[\/tex].\n<\/div>\n

\n

\n

Solu\u00e7\u00e3o<\/p>\n

\nVeja que <\/p>\n

[tex]\\qquad \\left(a+\\dfrac{2}{a}\\right)^3 = 2^3[\/tex]<\/p>\n

[tex]\\qquad a^3+3\\cdot a^2\\cdot \\left(\\dfrac{2}{a}\\right)+3\\cdot a\\cdot \\left(\\dfrac{2}{a}\\right)^2+\\left(\\dfrac{2}{a}\\right)^3= 8[\/tex]<\/p>\n

[tex]\\qquad a^3+6a+\\dfrac{12}{a}+\\dfrac{8}{a^3} = 8[\/tex]<\/p>\n

[tex]\\qquad a^3+\\dfrac{8}{a^3}+6a+\\dfrac{12}{a} = 8[\/tex]<\/p>\n

[tex]\\qquad a^3+\\dfrac{8}{a^3}+6\\left(a+\\dfrac{2}{a}\\right) = 8[\/tex]<\/p>\n

[tex]\\qquad a^3+\\dfrac{8}{a^3}+6\\cdot 2 = 8[\/tex]<\/p>\n

[tex]\\qquad \\boxed{a^3+\\dfrac{8}{a^3} = -4}.[\/tex]<\/p>\n

\n

Solu\u00e7\u00e3o elaborada pelos Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n

 <\/p>\n

\nParticiparam da discuss\u00e3o os Clubes Koreil Guys; Phidias; Pot\u00eancias de Euler<\/strong>.<\/div>\n

\n","protected":false},"excerpt":{"rendered":"

Problema (Indicado a partir do 8\u00ba ano do E. F.) Considere um n\u00famero [tex]a[\/tex], tal que [tex]a+\\dfrac{2}{a}=2[\/tex]. Determine o valor de [tex]a^3+\\dfrac{8}{a^3}[\/tex]. Solu\u00e7\u00e3o Veja que [tex]\\qquad \\left(a+\\dfrac{2}{a}\\right)^3 = 2^3[\/tex] [tex]\\qquad a^3+3\\cdot a^2\\cdot \\left(\\dfrac{2}{a}\\right)+3\\cdot a\\cdot \\left(\\dfrac{2}{a}\\right)^2+\\left(\\dfrac{2}{a}\\right)^3= 8[\/tex] [tex]\\qquad a^3+6a+\\dfrac{12}{a}+\\dfrac{8}{a^3} = 8[\/tex] [tex]\\qquad a^3+\\dfrac{8}{a^3}+6a+\\dfrac{12}{a} = 8[\/tex] [tex]\\qquad a^3+\\dfrac{8}{a^3}+6\\left(a+\\dfrac{2}{a}\\right) = 8[\/tex] [tex]\\qquad a^3+\\dfrac{8}{a^3}+6\\cdot 2 = 8[\/tex] [tex]\\qquad \\boxed{a^3+\\dfrac{8}{a^3} … <\/p>\n

Continue lendo<\/a><\/p>\n","protected":false},"author":254,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-224195","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/224195","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/254"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=224195"}],"version-history":[{"count":4,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/224195\/revisions"}],"predecessor-version":[{"id":224494,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/224195\/revisions\/224494"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=224195"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}