\(x^2\left(y^2-1\right)-x+y^2-3=0\)
Đặt \(y^2-1=a\)
\(\Leftrightarrow ax^2-x+a-2=0\)
\(\Delta=1-4a\left(a-2\right)=-4a^2+8a+1\ge0\)
\(\Rightarrow\frac{2-\sqrt{5}}{2}\le a\le\frac{2+\sqrt{5}}{2}\Rightarrow\frac{4-\sqrt{5}}{2}\le y^2\le\frac{4+\sqrt{5}}{2}\)
Do \(y\) nguyên \(\Rightarrow1\le y^2\le3\Rightarrow y^2=1\Rightarrow y=\pm1\Rightarrow x=-2\)