ĐKXĐ: \(x\ge-3\)
\(\Leftrightarrow x^2+1+2\left(x+3\right)-3\sqrt{\left(x^2+1\right)\left(x+3\right)}=0\)
Đặt \(\left\{{}\begin{matrix}\sqrt{x^2+1}=a>0\\\sqrt{x+3}=b\ge0\end{matrix}\right.\)
\(\Rightarrow a^2+2b^2-3ab=0\)
\(\Leftrightarrow\left(a-b\right)\left(a-2b\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=b\\a=2b\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x^2+1}=\sqrt{x+3}\\\sqrt{x^2+1}=2\sqrt{x+3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+1=x+3\\x^2+1=4x+12\end{matrix}\right.\)
\(\Leftrightarrow...\)
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