{"id":153787,"date":"2020-05-11T21:46:56","date_gmt":"2020-05-12T00:46:56","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=153787"},"modified":"2023-06-14T04:07:31","modified_gmt":"2023-06-14T07:07:31","slug":"probleminha-uma-expressao-potente-e-atual","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/probleminha-uma-expressao-potente-e-atual\/","title":{"rendered":".Probleminha: Uma express\u00e3o potente e atual!"},"content":{"rendered":"

\n

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Problema
\n (Indicado a partir do 7\u00ba ano do E. F.)<\/span><\/p>\n

\n

(Extra\u00eddo do material do PECI\/OBMEP<\/strong>)<\/span> Se [tex]\\boxed{2^{2020}\u22122^{2019}-2^{2018}+2^{2017}=k \\cdot 2^{2017}}[\/tex], qual o valor de [tex]k[\/tex]?<\/p>\n

\n<\/div>\n

\n

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

\n

Vamos reescrever a express\u00e3o dada no problema desta forma:
\n[tex]\\qquad \\qquad k\\cdot 2^{2017}=2^3 \\cdot 2^{2017}+2^{2017}\u22122^2 \\cdot 2^{2017}-2^1 \\cdot 2^{2017}.[\/tex]
\nDa\u00ed, segue que:
\n[tex]\\qquad k\\cdot 2^{2017}=8 \\cdot 2^{2017}+2^{2017}\u22124 \\cdot 2^{2017}-2 \\cdot 2^{2017}[\/tex]
\n[tex]\\qquad k\\cdot 2^{2017}=9 \\cdot 2^{2017}\u22126 \\cdot 2^{2017}[\/tex]
\n[tex]\\qquad k\\cdot 2^{2017}=3 \\cdot 2^{2017}.[\/tex]
\nPortanto, [tex]\\,\\fcolorbox{black}{#eee0e5}{$k=3$}\\,[\/tex].<\/p>\n

\n

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

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

Problema (Indicado a partir do 7\u00ba ano do E. F.) (Extra\u00eddo do material do PECI\/OBMEP) Se [tex]\\boxed{2^{2020}\u22122^{2019}-2^{2018}+2^{2017}=k \\cdot 2^{2017}}[\/tex], qual o valor de [tex]k[\/tex]? Solu\u00e7\u00e3o Vamos reescrever a express\u00e3o dada no problema desta forma: [tex]\\qquad \\qquad k\\cdot 2^{2017}=2^3 \\cdot 2^{2017}+2^{2017}\u22122^2 \\cdot 2^{2017}-2^1 \\cdot 2^{2017}.[\/tex] Da\u00ed, segue que: [tex]\\qquad k\\cdot 2^{2017}=8 \\cdot 2^{2017}+2^{2017}\u22124 \\cdot 2^{2017}-2 \\cdot … <\/p>\n

Continue lendo<\/a><\/p>\n","protected":false},"author":164,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-153787","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/153787","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\/164"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=153787"}],"version-history":[{"count":12,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/153787\/revisions"}],"predecessor-version":[{"id":194507,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/153787\/revisions\/194507"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=153787"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}