\(\sqrt{x\left(x-1\right)}+\sqrt{x\left(x+2\right)}=2\sqrt{x^2}\)
\(Đk\left[{}\begin{matrix}x\ge1\\x=0\\x\le-2\end{matrix}\right.\)
\(Pt:\Leftrightarrow x^2-x+2\sqrt{x^2\left(x-1\right)\left(x+2\right)}+x^2+2x=4x^2\)
\(\Leftrightarrow2\sqrt{x^2\left(x-1\right)\left(x+2\right)}=2x^2-x\)
\(\Leftrightarrow4x^2\left(x-1\right)\left(x+2\right)=4x^4-4x^3+x^2\)
\(\Leftrightarrow4x^4+4x^3-8x^2=4x^4-4x^3+x^2\)
\(\Leftrightarrow8x^3-9x^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\frac{9}{8}\end{matrix}\right.\left(tm\right)\)
