Question

Giải ptrinh : 

\(\sqrt[3]{x-1}+\sqrt[3]{x+1}=x\sqrt[3]{2}\)

Answer 1

\(\Leftrightarrow2x+3\sqrt[3]{x^2-1}\left(\sqrt[3]{x-1}+\sqrt[3]{x+1}\right)=2x^3\)

\(\Rightarrow2x+3\sqrt[3]{x^2-1}.x\sqrt[3]{2}=2x^3\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\2+3\sqrt[3]{2\left(x^2-1\right)}=2x^2\left(1\right)\end{matrix}\right.\)

Xét (1):

Đặt \(\sqrt[3]{2x^2-2}=t\Rightarrow2x^2=t^3+2\)

\(\Rightarrow2+3t=t^3+2\)

\(\Leftrightarrow t\left(t^2-3\right)=0\)

\(\Leftrightarrow...\)