Найти значение выражения [tex] (3-\sqrt{2}) \sqrt{17+6 \sqrt{4- \sqrt{9+4 \sqrt{2} } } } [/tex]. Created by yellok. algebra-ru

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yellok @yellok

July 2022 1 55 Report

Найти значение выражения
[tex] (3-\sqrt{2}) \sqrt{17+6 \sqrt{4- \sqrt{9+4 \sqrt{2} } } } [/tex]

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NeZeRAvix

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$(3- \sqrt{2}) \sqrt{17+ 6 \sqrt{4- \sqrt{9+4 \sqrt{2} } } } = \\ = \sqrt{(3- \sqrt{2})^2( 17+ 6 \sqrt{4- \sqrt{(1+2 \sqrt{2})^2 } })}}= \\ = \sqrt{(11-6 \sqrt{2})(17+ 6 \sqrt{3-2 \sqrt{2} } )} } = \\ = \sqrt{(11-6 \sqrt{2})(17+6 \sqrt{( \sqrt{2}-1)^2 }) } = \\ = \sqrt{(11-6 \sqrt{2})(11+6 \sqrt{2}) }= \\ = \sqrt{121-72}= \sqrt{49}=7$

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