`xy-2=x+y`
`=>xy-x=y+2`
`=>x(y-1)=y-1+3`
`=>(x-1)(y-1)=3`
Vì `x,y in ZZ=>x,y in ZZ`
`=>x-1,y-1 in Ư(3)={1,-1,3,-3}`
Ta có bảng sau:
| x-1 | 1 | -1 | 3 | -3 |
| y-1 | 3 | -3 | 1 | -1 |
| x | 2 | 0 | 4 | -2 |
| y | 4 | -2 | 2 | 0 |
| KL | TM | TM | TM | TM |
Vậy `(x,y) in (2,4),(0,-2),(4,2),(-2,0)`
Giải:
\(xy-2=x+y\)
\(\Rightarrow xy-x=y+2\)
\(\Rightarrow x.\left(y-1\right)=y-1+3\)
\(\Rightarrow x.\left(y-1\right)-\left(y-1\right)=3\)
\(\Rightarrow\left(x-1\right).\left(y-1\right)=3\)
\(\Rightarrow\left(x-1\right)\) và \(\left(y-1\right)\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)
Ta có bảng giá trị:
| x-1 | -3 | -1 | 1 | 3 |
| y-1 | -1 | -3 | 3 | 1 |
| x | -2 | 0 | 2 | 4 |
| y | 0 | -2 | 4 | 2 |
Vậy \(\left(x;y\right)=\left\{\left(-2;0\right);\left(0;-2\right);\left(2;4\right);\left(4;2\right)\right\}\)
Chúc bạn học tốt!
