Упростите выражение,если 1≤b≤2 [tex] \sqrt{(2- \sqrt{b}) ^{2}+8 \sqrt{b}}- \sqrt{(1+ \sqrt{b}) ^{2} -4 \sqrt{b}[/tex]. Created by UnDeadMoroz. algebra-ru

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September 2021 1 17 Report

Упростите выражение,если 1≤b≤2 [tex] \sqrt{(2- \sqrt{b}) ^{2}+8 \sqrt{b}}- \sqrt{(1+ \sqrt{b}) ^{2} -4 \sqrt{b}[/tex]

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mishka19 $\sqrt{(2- \sqrt{b})^2+8 \sqrt{b} }- \sqrt{(1+ \sqrt{b})^2-4 \sqrt{b} }= \\ = \sqrt{2^2-2*2* \sqrt{b} +(\sqrt{b})^2+8 \sqrt{b} }- \sqrt{1^2+2*1* \sqrt{b} + (\sqrt{b})^2-4 \sqrt{b} } \\ =\sqrt{2^2-4 \sqrt{b} +(\sqrt{b})^2+8 \sqrt{b} }- \sqrt{1^2+2 \sqrt{b} + (\sqrt{b})^2-4 \sqrt{b} } = \\ =\sqrt{2^2+4 \sqrt{b} +(\sqrt{b})^2 }- \sqrt{1^2-2 \sqrt{b} + (\sqrt{b})^2 } = \\ = \sqrt{(2+ \sqrt{b})^2 }- \sqrt{(1-\sqrt{b})^2 }=|2+ \sqrt{b}|-|1-\sqrt{b}|= \\ =2+ \sqrt{b}-(\sqrt{b}-1)=3$

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