Đáp án:
`2xy - x + y = -5 (x,y ∈ ZZ)`
`↔2 (2xy - x + y) = -5 × 2`
`↔ 4xy - 2x + 2y = -10`
`↔ 4xy - 2x + 2y - 1 = -10 - 1`
`↔ (4xy - 2x) + (2y - 1) = -11`
`↔ 2x (2y - 1) + (2y - 1) =-11`
`↔ (2x + 1) (2y-1) = -11`
Ta có bảng :
$\begin{array}{|c|c|c|c|c|c|c|}\hline 2x+1& -1 & 11 & 1 & -11\\\hline 2y-1& 11 & -1 & -11 & 1 \\\hline x & -1&5&0&-6\\\hline y & 6&0&-5&1 \\\hline\end{array}$
Vậy cặp `(x;y)` nguyên là : `(-1;6), (0;5), (0;-5), (-6;1)`
