Упростите выражение:(√5-2)/(√5+2). Created by AnyaMikayilova. matematika-ru

(√5+2)...

AnyaMikayilova @AnyaMikayilova

July 2022 2 37 Report

Упростите выражение:(√5-2)/(√5+2)

ПрофиЗнания

Verified answer

(√5-2)(√5-2)/(√5+2)(√5-2) = (5-4√5+4) / (5-4) =(9-4√5) /1 =9-4√5

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matilda17562

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Решение:

$\frac{\sqrt{5} - 2}{\sqrt{5} + 2} = \frac{(\sqrt{5} - 2)*(\sqrt{5} - 2)}{(\sqrt{5} + 2)*(\sqrt{5} - 2)} =$ $\frac{(\sqrt{5} - 2)^{2}}{(\sqrt{5}) ^{2} - 2^{2}} = \frac{5 + 4 - 4\sqrt{5} }{5 - 4} = 9 - 4\sqrt{5} .$

Ответ: $9 - 4\sqrt{5}$ .

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