Question

Tím x, y thuộc Z thỏa mãn: xy+x-y=4

Answer 1

\(xy+x-y=4\\ \Rightarrow xy+x-y-1+1=4\\ \Rightarrow\left(xy+x\right)-\left(y+1\right)=4-1\\ \Rightarrow x\left(y+1\right)-\left(y+1\right)=3\\ \Rightarrow\left(x-1\right)\left(y+1\right)=3\\ \Rightarrow\left(x-1\right);\left(y+1\right)\inƯ\left(3\right)\\ \Rightarrow\left(x-1\right);\left(y+1\right)\in\left\{-3;-1;1;3\right\}\)

\(x-1\)	\(-3\)	\(-1\)	\(1\)	\(3\)
\(y+1\)	\(-1\)	\(-3\)	\(3\)	\(1\)
\(x\)	\(-2\)	\(0\)	\(2\)	\(4\)
\(y\)	\(-2\)	\(-4\)	\(2\)	\(0\)

 

Vậy \(\left(x;y\right)=\left(-2;-2\right),\left(0;-4\right),\left(2;2\right),\left(4,0\right)\)