Question

giải phương trình:

\(\sqrt{x\left(x+1\right)}+\sqrt{x\left(x+2\right)}=\sqrt{x\left(x-3\right)}\)

Answer 1

\(\Leftrightarrow\sqrt{x}\left(\sqrt{x+1}+\sqrt{x+2}-\sqrt{x-3}\right)=0\)

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\\sqrt{4x^2+12x+8}=-x-6\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\\left\{{}\begin{matrix}x< =-6\\4x^2+12x+8=x^2+12x+36\end{matrix}\right.\end{matrix}\right.\Leftrightarrow x=0\)