Question

Tìm cặp x,y nguyên thỏa mãn 

xy+6=2.(x+y)

 

Answer 1

xy+6=2(x+y)

=>xy-2x-2y+6=0

=>x(y-2)-2y+4+2=0

=>x(y-2)-2(y-2)=-2

=>(x-2)(y-2)=-2

=>\(\left(x-2\right)\cdot\left(y-2\right)=1\cdot\left(-2\right)=\left(-2\right)\cdot1=\left(-1\right)\cdot2=2\cdot\left(-1\right)\)

=>\(\left(x-2;y-2\right)\in\left\{\left(1;-2\right);\left(-2;1\right);\left(-1;2\right);\left(2;-1\right)\right\}\)

=>\(\left(x,y\right)\in\left\{\left(3;0\right);\left(0;3\right);\left(1;4\right);\left(4;1\right)\right\}\)