упростите выражение [tex] \sqrt{7-2 \sqrt{6} } + \sqrt{7+2 \sqrt{6} } [/tex]. Created by Miku03. algebra-ru

tex]...

Miku03 @Miku03

July 2022 1 7 Report

упростите выражение
[tex] \sqrt{7-2 \sqrt{6} } + \sqrt{7+2 \sqrt{6} } [/tex]

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Artem112

Verified answer

$\sqrt{7-2 \sqrt{6} } + \sqrt{7+2 \sqrt{6} } =
\\\
= \sqrt{( \sqrt{6})^2 -2\cdot \sqrt{6}\cdot1+1^2 } + \sqrt{( \sqrt{6})^2 +2\cdot \sqrt{6}\cdot1+1^2} =
\\\
= \sqrt{( \sqrt{6}-1)^2} + \sqrt{( \sqrt{6}+1)^2} 
=| \sqrt{6}-1| + | \sqrt{6}+1|=
\\\
= \sqrt{6}-1 + \sqrt{6}+1=2 \sqrt{6}$

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Miku03 August 2022 | 0 Ответы

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