Question

Tính
\(\sqrt[3]{182+\sqrt{33125}}+\sqrt[3]{182-\sqrt{33125}}\)

Answer 1

Đặt \(x=\sqrt[3]{182+\sqrt[]{33125}}+\sqrt[3]{182-\sqrt[]{33125}}\)

\(\Rightarrow x^3=364+3\sqrt[3]{182^2-33125}.\left(\sqrt[3]{182+\sqrt[]{33125}}+\sqrt[]{182-\sqrt[]{33125}}\right)\)

\(\Rightarrow x^3=364+3.\left(-1\right).x\)

\(\Rightarrow x^3+3x-364=0\)

\(\Rightarrow\left(x-7\right)\left(x^2+7x+52\right)=0\)

\(\Rightarrow x-7=0\) (do \(x^2+7x+52>0;\forall x\))

\(\Rightarrow x=7\)