ĐK:\(x^2-2x+3\ge0\)(*)
\(PT\Leftrightarrow\left(x+1\right)\left(\sqrt{x^2-2x+3}-2\right)-x^2+2x+1=0\)
\(\Leftrightarrow\left(x+1\right).\frac{x^2-2x-1}{\sqrt{x^2-2x+3}+2}-x^2+2x+1=0\)
\(\Leftrightarrow\left(x^2-2x-1\right).\left(\frac{x+1}{\sqrt{x^2-2x+3}+2}-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\pm\sqrt{2}\left(tm\right)\\x+1=\sqrt{x^2-2x+3}+2\end{matrix}\right.\)
+\(x-1=\sqrt{x^2-2x+3}\Leftrightarrow\) \(\left\{{}\begin{matrix}x\ge1\\x^2-2x+1=x^2-2x+3\left(vl\right)\end{matrix}\right.\)
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