\(\left(y-x\right)^2-4\left(y-x\right)=x^2-4x\)
\(\Leftrightarrow\left(y-x\right)^2-4\left(y-x\right)+4=x^2-4x+4\)
\(\Leftrightarrow\left(y-x-2\right)^2=\left(x-2\right)^2\)
\(\Leftrightarrow\left[{}\begin{matrix}y-x-2=x-2\\y-x-2=2-x\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}y=2x\\y=4\end{matrix}\right.\)
- Với \(y=4\Rightarrow4\sqrt[3]{x^2-4}=6\Rightarrow x^2=\frac{59}{8}\)
- Với \(y=2x\)
\(x\left(2x-4\right)+4\sqrt[3]{x^2-2x}=6\)
\(\Leftrightarrow\left(x^2-2x\right)+2\sqrt[3]{x^2-2x}-3=0\)
Đặt \(\sqrt[3]{x^2-2x}=a\)
\(\Rightarrow a^3+2a-3=0\Rightarrow a=1\)
\(\Rightarrow\sqrt[3]{x^2-2x}=1\Leftrightarrow x^2-2x=1\)