\(\sqrt{x^2+3x-2}=\sqrt{1+x}\)
\(\Leftrightarrow\left\{{}\begin{matrix}1+x\ge0\\x^2+3x-2=1+x\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\x^2+2x-3=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\\left[{}\begin{matrix}x=1\\x=-3\left(loại\right)\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow x=1\)