tex] Заранее большое спасибо!!...

Yulia20000 @Yulia20000

July 2022 1 4 Report

Помогите решить!!
Нужно вычислить(10-11 класс)

[tex] \sqrt{29-12 \sqrt{5} } - \sqrt{29+12 \sqrt{5} } [/tex]

Заранее большое спасибо!!

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Banabanana

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$\sqrt{29-12 \sqrt{5} } - \sqrt{29+12 \sqrt{5} } = \sqrt{9-12 \sqrt{5}+20 } - \sqrt{9+12 \sqrt{5}+20 }= \\\\ = \sqrt{9-12 \sqrt{5}+2 \sqrt{5} } - \sqrt{9+12 \sqrt{5}+2 \sqrt{5} }= \\\\ =\sqrt{(3-2 \sqrt{5})^2 } - \sqrt{(3+2 \sqrt{5})^2 }=|3-2 \sqrt{5}|-(3+2 \sqrt{5} )= \\\\ =2 \sqrt{5}-3-3-2 \sqrt{5}= -6$

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