Question

tìm x,y thuộc Z sao cho xy=2x+2y

Answer 1

\(xy=2x+2y\\ \Rightarrow xy-2x-2y=0\\ \Rightarrow x\left(y-2\right)-2y+4=4\\ \Rightarrow x\left(y-2\right)-2\left(y-2\right)=4\\ \Rightarrow\left(x-2\right)\left(y-2\right)=4\)

Vì \(x,y\in Z\Rightarrow\left\{{}\begin{matrix}x-2,y-2\in Z\\x-2,y-2\inƯ\left(4\right)\end{matrix}\right.\)

Ta có bảng:

x-2	-1	-2	-4	1	2	4
y-2	-4	-2	-1	4	2	1
x	1	0	-2	3	4	6
y	-2	0	1	6	4	3

Vậy \(\left(x,y\right)\in\left\{\left(1;-2\right);\left(0;0\right);\left(-2;1\right);\left(3;6\right);\left(4;4\right);\left(6;3\right)\right\}\)