ĐKXĐ: \(x\ge\frac{3+\sqrt{41}}{4}\)
\(\Leftrightarrow x+x^2-1+2\sqrt{x\left(x^2-1\right)}=2x^2-3x-4\)
\(\Leftrightarrow2\sqrt{x\left(x^2-1\right)}=x^2-4x-3\)
\(\Leftrightarrow2\sqrt{\left(x^2-x\right)\left(x+1\right)}=x^2-4x-3\)
Đặt \(\left\{{}\begin{matrix}\sqrt{x^2-x}=a>0\\\sqrt{x+1}=b>0\end{matrix}\right.\)
\(\Rightarrow2ab=a^2-3b^2\)
\(\Leftrightarrow a^2-2ab-3b^2=0\)
\(\Leftrightarrow\left(a+b\right)\left(a-3b\right)=0\)
\(\Leftrightarrow a=3b\)
\(\Leftrightarrow x^2-x=9\left(x+1\right)\)
\(\Leftrightarrow x^2-10x-9=0\)
