упростите√√17+12√2Всё под первым корнем. Created by Apxangel. algebra-ru

упростите√√17+12√2Всё под первым корнем...

Vladislav006

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Решение ниже в приложении

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mmb1

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$\sqrt{ \sqrt{17+12 \sqrt{2} }}= \sqrt{ \sqrt{9+12 \sqrt{2}+8 }}= \\ \sqrt{ \sqrt{3^2+2*3*2 \sqrt{2}+(2 \sqrt{2} )^2 }}= \\ \sqrt{ \sqrt{(3+2 \sqrt{2})^2 }}= \sqrt{3+2 \sqrt{2} }= \sqrt{1^2+2 \sqrt{2}+ \sqrt{2}^2 } = \\ \sqrt{( \sqrt{2}+1 )^2} = \sqrt{2}+1$

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