Помогите, пожалуйста)√9-4√5

August 2022 2 12 Report

Помогите, пожалуйста)
√9-4√5 - √9+4√5

NNNLLL54

Verified answer

$\sqrt{9-4\sqrt5}-\sqrt{9+4\sqrt5}=\sqrt{(2-\sqrt5)^2}-\sqrt{(2+\sqrt5)^2}=\\\\=|2-\sqrt5|-|2+\sqrt5|=2-\sqrt5-2-\sqrt5=-2\sqrt5$

Замечание:
$9-4\sqrt5=4-4\sqrt5+5=(2-\sqrt5)^2$

4 votes Thanks 2

NNNLLL54 9=4+5

mmb1

Verified answer

√9-4√5 - √9+4√5=√(√5-2)²-√(√5+2)²=√5-2-√5-2=-4
9-4√5=5-2*2*√5+4=(√5-2)²

3 votes Thanks 1

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