PT \(\Leftrightarrow2x^2-2-5\sqrt{x^2+1}+1=0\)
\(\Leftrightarrow2x^2+2-5\sqrt{x^2+1}-3=0\)
\(\Leftrightarrow2\left(\sqrt{x^2+1}\right)^2-5\sqrt{x^2+1}-3=0\)
\(\Leftrightarrow\sqrt{x^2+1}=3\)
\(\Leftrightarrow x^2+1=9\)
\(\Leftrightarrow x=2\sqrt{2}\)
Vậy ...
\(2\left(x-1\right)\left(x+1\right)-5\sqrt{x^2+1}+1=0\\ \Leftrightarrow2\left(x^2-1\right)-5\sqrt{x^2+1}+1=0\\ \Leftrightarrow2x^2-2-5\sqrt{x^2+1}+1=0\\ \Leftrightarrow2x^2+2-5\sqrt{x^2+1}-3=0\\ \Leftrightarrow2\left(x^2+1\right)-5\sqrt{x^2+1}-3=0\)
Đặt \(\sqrt{x^2+1}=t\left(t\ge1\right)\Rightarrow x+1=t^2\)
\(PT\Leftrightarrow2t^2-5t-3=0\\ \Leftrightarrow2t^2-6t+t-3=0\\ \Leftrightarrow2t\left(t-3\right)+\left(t-3\right)=0\\ \Leftrightarrow\left(t-3\right)\left(2t-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}t=3\left(n\right)\\t=-\dfrac{1}{2}\left(l\right)\end{matrix}\right.\\ \Leftrightarrow\sqrt{x^2+1}=3\\ \Leftrightarrow x^2+1=9\\ \Leftrightarrow x^2=8\\ \Leftrightarrow x=\pm2\sqrt{2}\)
Vậy \(x\in\left\{2\sqrt{2};-2\sqrt{2}\right\}\)
