tex] Идеи нет никаких...

July 2022 2 2 Report

Как упростить это выражение, чтобы получилось 1???
[tex] \frac{2- \sqrt{2} - \sqrt{6+4 \sqrt{2} } }{4} [/tex]
Идеи нет никаких.

dtnth

Verified answer

$\sqrt{6+4\sqrt{2}}=\sqrt{4+4\sqrt{2}+2}=\\\\\sqrt{2^2+2*2*\sqrt{2}}+(\sqrt{2})^2}=\sqrt{(2+\sqrt{2})^2}=|2+\sqrt{2}|=2+\sqrt{2}$
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$\frac{2-\sqrt{2}-\sqrt{6+4\sqrt{2}}}{4}=\frac{2-\sqrt{2}-2-\sqrt{2}}{4}=-\frac{\sqrt{2}}{2}$

если же!!!!
$\frac{2-\sqrt{2}+\sqrt{6+4\sqrt{2}}}{4}=\frac{2-\sqrt{2}+2+\sqrt{2}}{4}=1$

1 votes Thanks 1

Матов

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$\frac{2-\sqrt{2}-\sqrt{6+4\sqrt{2}}}{4}=\frac{2-\sqrt{2}-\sqrt{(2+\sqrt{2})^2}}{4}\\
 \frac{2-\sqrt{2}-2-\sqrt{2}}{4}=\frac{-2\sqrt{2}}{4}=\frac{-\sqrt{2}}{2}$
Ответ 1 неверен

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