tex]...

August 2022 1 14 Report

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Найдите значение выражения
[tex] \frac{ \sqrt[5]{(5 \sqrt{2} +7)^{4} } }{ \sqrt[5]{7- 5\sqrt{2} } } +8[/tex]

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NNNLLL54

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$\frac{\sqrt[5]{(5\sqrt2+7)^4}}{\sqrt[5]{7-5\sqrt2}} +8=\frac{\sqrt[5]{(5\sqrt2+7)^5}}{\sqrt[5]{(7-5\sqrt2)(7+5\sqrt2)}}+8= \frac{5\sqrt2+7}{\sqrt[5]{49-25\cdot 2}} +8=\\\\= \frac{5\sqrt2+7}{-1} +8=-5\sqrt2-7+8=1-5\sqrt2$

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