Question

[MN Hướng Dương]

$x=\root(3)(22\sqrt(2+)25-\root(3)(22\sqrt(2))- 25)$

Answer 1

[Nguyễn Hoàng Minh]

Đặt \(A=\sqrt[3]{22\sqrt{2}+25}-\sqrt[3]{22\sqrt{2}-25}\)

\(\Rightarrow A^3=50-3\sqrt[3]{\left(22\sqrt{2}+25\right)\left(22\sqrt{2}-25\right)}\left(\sqrt[3]{22\sqrt{2}+25}-\sqrt[3]{22\sqrt{2}-25}\right)\)

\(\Rightarrow A^3=50-3\sqrt[3]{\left(22\sqrt{2}+25\right)\left(22\sqrt{2}-25\right)}\cdot A\)

\(\Rightarrow A^3=50-3A\sqrt[3]{343}=50-21A\)

\(\Rightarrow A^3+21A-50=0\Leftrightarrow A^3-4A+25A-50=0\)

\(\Leftrightarrow\left(A-2\right)\left(A^2+2A+25\right)=0\)

\(\Leftrightarrow A=2\left(A^2+2A+25>0,\forall A\right)\)

\(\Rightarrow\sqrt[3]{22\sqrt{2}+25}-\sqrt[3]{22\sqrt{2}-25}=2\)

Tick nha bạn 😘