\(x+y=xy\)
\(\Rightarrow xy-x-y=0\)
\(\Rightarrow x\left(y-1\right)-y=0\)
\(\Rightarrow x\left(y-1\right)-y+1=1\)
\(\Rightarrow x\left(y-1\right)-\left(y-1\right)=1\)
\(\Rightarrow\left(x-1\right)\left(y-1\right)=1\)
\(\Rightarrow x-1=1;y-1=1\) hoặc \(x-1=-1;y-1=-1\)
+) \(x-1=1\Rightarrow x=2\)
\(y-1=1\Rightarrow y=2\)
+) \(x-1=-1\Rightarrow x=0\)
\(y-1=-1\Rightarrow y=0\)
Vậy cặp số \(\left(x;y\right)\) là \(\left(2;2\right);\left(0;0\right)\)
Ta có x+y=xy
\(\Leftrightarrow\) x+y-1=xy-1
\(\Leftrightarrow x+y-1-xy=-1\)
\(\Leftrightarrow\left(y-1\right)\left(1-x\right)=-1\)
Ta lập bảng
| y-1= | 1-x= | y= | x= |
| -1 | 1 | 0 | 0 |
| 1 | -1 | 2 | 2 |
Vậy cặp số (x,y) là (0;0);(2;2)
