\(xy^2-2xy+x+y^2=6\Leftrightarrow x\left(y^2-2y+1\right)+y^2-1=5\)
\(\Leftrightarrow x\left(y-1\right)^2+\left(y-1\right)\left(y+1\right)=5\)
\(\Leftrightarrow\left(y-1\right)\left(xy-x+y+1\right)=5\)
\(Ư\left(5\right)=\left(-5;-1;1;5\right)\)
| y-1 | -5 | -1 | 1 | 5 |
| y | -4 | 0 | 2 | 6 |
| xy-x+y+1 | -1 | -5 | 5 | 1 |
| x | -2/5 | 6 | 2 | -6/5 |
Vì \(x;y\in Z\Rightarrow\left[{}\begin{matrix}\left(x;y\right)=\left(6;0\right)\\\left(x;y\right)=\left(2;2\right)\end{matrix}\right. \)
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