Ta có : \(\frac{1}{x}+\frac{1}{y}+\frac{2}{xy}=1\)
=> \(\frac{y}{xy}+\frac{x}{xy}+\frac{2}{xy}=1\)
=> \(\frac{y+x+2}{xy}=1\)
=> y + x + 2 = xy
=> y + x + 2 - xy = 0
=> y(1 - x) + x + 2 = 0
=> y(1 - x) + (1 - x) = -3
=> (y + 1)(1 - x) = -3
=> x, y \(\in\)Ư (-3) = {1; -1; 3; -3}
Lập bảng :
y + 1 | 1 | -1 | 3 | -3 |
1 - x | -3 | 3 | -1 | 1 |
y | 0 | -2 | 2 | -4 |
x | 4 | -2 | 2 | 0 |
Vậy ...