{"id":210790,"date":"2024-02-01T17:59:03","date_gmt":"2024-02-01T20:59:03","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=210790"},"modified":"2024-02-01T19:59:20","modified_gmt":"2024-02-01T22:59:20","slug":"problema-texsqrt2a1-tex","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/problema-texsqrt2a1-tex\/","title":{"rendered":".Problema: [tex]\\sqrt{2a+1}[\/tex]"},"content":{"rendered":"

✏ Link do problema para dispositivos da Apple<\/em>.<\/span><\/a><\/strong><\/p>\n

\n

Problema
\n (Indicado a partir do 9\u00ba ano do E. F.)<\/span><\/p>\n

\nSabendo que [tex]\\boxed{a+1 = 2021^2+2022^2}[\/tex], determine o valor de [tex]\\sqrt{2a+1~}.[\/tex]\n<\/div>\n

 <\/p>\n

\n

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

\nVeja que:
\n[tex] \\qquad \\qquad \\begin{align}
\n\\sqrt{2a+1~} &= \\sqrt{2(a+1)-1~}\\\\
\n&= \\sqrt{2\\left(2021^2+2022^2\\right)-1~}\\\\
\n&= \\sqrt{2\\left[2021^2+(2021+1)^2\\right]-1~}\\\\
\n&= \\sqrt{2\\left[2021^2+2021^2+2\\cdot 2021+1\\right]-1~}\\\\
\n&= \\sqrt{4\\cdot 2021^2+4\\cdot 2021+1~}\\\\
\n&= \\sqrt{(2\\cdot 2021+1)^2~}\\\\
\n&= \\sqrt{4043^2~}\\\\
\n&= 4043.
\n\\end{align}[\/tex]<\/p>\n
\n

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

 <\/p>\n

\nParticipou da discuss\u00e3o o Clube Phidias<\/strong>.<\/div>\n

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

✏ Link do problema para dispositivos da Apple. Problema (Indicado a partir do 9\u00ba ano do E. F.) Sabendo que [tex]\\boxed{a+1 = 2021^2+2022^2}[\/tex], determine o valor de [tex]\\sqrt{2a+1~}.[\/tex]   Solu\u00e7\u00e3o Veja que: [tex] \\qquad \\qquad \\begin{align} \\sqrt{2a+1~} &= \\sqrt{2(a+1)-1~}\\\\ &= \\sqrt{2\\left(2021^2+2022^2\\right)-1~}\\\\ &= \\sqrt{2\\left[2021^2+(2021+1)^2\\right]-1~}\\\\ &= \\sqrt{2\\left[2021^2+2021^2+2\\cdot 2021+1\\right]-1~}\\\\ &= \\sqrt{4\\cdot 2021^2+4\\cdot 2021+1~}\\\\ &= \\sqrt{(2\\cdot 2021+1)^2~}\\\\ &= \\sqrt{4043^2~}\\\\ … <\/p>\n

Continue lendo<\/a><\/p>\n","protected":false},"author":254,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-210790","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/210790","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=210790"}],"version-history":[{"count":6,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/210790\/revisions"}],"predecessor-version":[{"id":212202,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/210790\/revisions\/212202"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=210790"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}