Question

Giải phương trình

\(x\sqrt{x}-2\sqrt{x}-x=0\)

Answer 1

ĐK:\(x\ge0\)

\(x\sqrt{x}-2\sqrt{x}-x=0\Leftrightarrow\sqrt{x}\left(x-2-\sqrt{x}\right)=0\Leftrightarrow\sqrt{x}\left(x-2\sqrt{x}+\sqrt{x}-2\right)=0\Leftrightarrow\sqrt{x}\left[\sqrt{x}\left(\sqrt{x}-2\right)+\left(\sqrt{x}-2\right)\right]=0\Leftrightarrow\sqrt{x}\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)=0\Leftrightarrow\)\(\left[{}\begin{matrix}\sqrt{x}=0\\\sqrt{x}-2=0\\\sqrt{x}+1=0\end{matrix}\right.\)\(\Leftrightarrow\)\(\left[{}\begin{matrix}\sqrt{x}=0\\\sqrt{x}=2\\\sqrt{x}=-1\left(loai\right)\end{matrix}\right.\)\(\Leftrightarrow\)\(\left[{}\begin{matrix}x=0\left(tm\right)\\x=4\left(tm\right)\end{matrix}\right.\)

Vậy S={0;4}