tex]...

aruukest @aruukest

July 2022 1 2 Report

упростите
[tex] \sqrt[3]{?} \sqrt[4]{52} + \sqrt{5} \times \sqrt[3]{?} \sqrt[4]{52} - \sqrt{5} [/tex]

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Jikarinkite

$\sqrt[3]{ \sqrt[4]{52 } + \sqrt{5} } \times \sqrt[3]{5 + 2 \sqrt{13} } \times \sqrt[3]{ \sqrt[4]{52} - \sqrt{5} } = \\ = \sqrt[3]{( \sqrt[4]{52} + \sqrt{5} )(5 + 2 \sqrt{13})( \sqrt[4]{52} - \sqrt{5} ) } = \\ = \sqrt[3]{( \sqrt{52} - 5)(5 + 2 \sqrt{13}) } = \sqrt[3]{(2 \sqrt{13} - 5)(2 \sqrt{13} + 5) } = \sqrt[3]{52 - 25} = \\ = \sqrt[3]{27} = 3$

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