СРОЧНО,60Б УПРОСТИТЕ ВЫРАЖЕНИЕ (3√10+1)*(√5/√8+√5 - √2/√5-√8). Created by vikulyaabbasova. algebra-ru

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vikulyaabbasova @vikulyaabbasova

July 2022 1 10 Report

СРОЧНО,60Б
УПРОСТИТЕ ВЫРАЖЕНИЕ (3√10+1)*(√5/√8+√5 - √2/√5-√8)

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NNNLLL54

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$(3\sqrt{10}+1)( \frac{\sqrt5}{\sqrt8+\sqrt5}-\frac{\sqrt2}{\sqrt5-\sqrt8})=\\\\=(3\sqrt{10}+1)\cdot \frac{5-\sqrt{40}-\sqrt{16}-\sqrt{10}}{(\sqrt5-\sqrt8)(\sqrt5+\sqrt8)} =\\\\=(3\sqrt{10}+1)\cdot \frac{5-2\sqrt{10}-4-\sqrt{10}}{5-8} =(1+3\sqrt{10})\cdot \frac{1-3\sqrt{10}}{-3} =\\\\= \frac{1^2-(3\sqrt{10})^2}{-3} =-\frac{1-9\cdot 10}{3} =- \frac{-89}{3} = \frac{89}{3} =29\frac{2}{3}$

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