Question

Определите, верно ли равенство:
$sqrt[3]{9 + sqrt{80} } + sqrt[3]{9 - sqrt{80} } = 3$

Answer 1

$tt sqrt[3]{9+sqrt{80}}+sqrt[3]{9-sqrt{80}}=sqrt[3]{9+4sqrt{5}}+sqrt[3]{9-4sqrt{5}}=\ \ \ =sqrt[3]{(1.5+0.5sqrt{5})^3}+sqrt[3]{(1.5-0.5sqrt{5})^2} =1.5+0.5sqrt{5}+1.5-0.5sqrt{5}=3$

Да, верно