Question

вычеслите √(14 + 6 × √5) – √(9 – 4 × √5)

Answer 1

$sqrt{14+6sqrt{5}}=sqrt{9+6sqrt{5}+5}=\\sqrt{3^2+2*3*sqrt{5}+(sqrt{5})^2}=\\sqrt{(3+sqrt{5})^2=\\|3+sqrt{5}|=3+sqrt{5}$
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$sqrt{9-4sqrt{5}}=sqrt{4-4sqrt{5}+5}=\\sqrt{2^2-2*2*sqrt{5}+(sqrt{5})^2}=\\sqrt{(2-sqrt{5})^2}=\\|2-sqrt{5}|=sqrt{5}-2$
так как
$2-sqrt{5}=sqrt{4}-sqrt{5}<0$
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$sqrt{14+6sqrt{5}}-sqrt{9-4sqrt{5}}=(3+sqrt{5})-(sqrt{5}-2)=\\3+sqrt{5}-sqrt{5}+2=5$
ответ: 5