`x+10y+2xy+1=0`

`<=>x+(10y+2xy)=0-1`

`<=>x+2y(x+5)=-1`

`<=>x+5+2y(x+5)=-1+5`

`<=>1(x+5)+2y(x+5)=4`

`<=>(x+5)(2y+1)=4`

Vì `x,y in ZZ`

`=>x+5;2y+1 in Ư(4)={+-1;+-2;+-4}`

Mà `2y+1` là số nguyên lẻ

`=>2y+1 in {+-1}`

Ta có bảng sau:

\begin{array}{|c|c|c|}\hline \text{$x+5$}&\text{4}&\text{$-4$}\\\hline \text{$x$}&\text{$-1$}&\text{$-9$}\\\hline \text{$2y+1$}&\text{1}&\text{$-1$}\\\hline \text{$2y$}&\text{0}&\text{$-2$}\\\hline \text{$y$}&\text{0}&\text{$-1$}\\\hline\end{array}

Vậy `(x,y) in {(-1;0);(-9;-1)}`