\(x+xy+y=12\Leftrightarrow x\left(y+1\right)+y=12\)
\(\Leftrightarrow x\left(y+1\right)+y+1=12+1\)
\(\Leftrightarrow\left(x+1\right)\left(y+1\right)=13\)
\(\Rightarrow x+1;y+1\inƯ\left(13\right)\Rightarrow x+1;y+1\in\left\{\pm1;\pm13\right\}\)
Ta có bảng sau :
x + 1 | 1 | -1 | 13 | -13 |
y + 1 | 13 | -13 | 1 | 1 |
x | 0 | -2 | 12 | -14 |
y | 12 | -14 | 0 | -2 |
Vậy các cặp số (x;y) là : (0;12) ; (-2;-14) ; (12;0) ; (-14;-2)