\(\Leftrightarrow4x^2+2x\left(\sqrt{x^2+1}-x\right)=3=0\)
\(\Leftrightarrow2x^2+2x\sqrt{x^2+1}-3=0\)
\(\Leftrightarrow x^2+2x\sqrt{x^2+1}+x^2+1=4\)
\(\Leftrightarrow\left(x+\sqrt{x^2+1}\right)^2=4\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\sqrt{x^2+1}=4\\x+\sqrt{x^2-1}=-4\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x^2+1}=4-x\left(x\le4\right)\\\sqrt{x^2+1}=-4-x\left(x\le-4\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+1=\left(4-x\right)^2\\x^2+1=\left(-4-x\right)^2\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}8x=15\\8x=-15\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{15}{8}\\x=-\frac{15}{8}\left(l\right)\end{matrix}\right.\)
