Question

Tìm cặp số nguyên x, y biết: x + y = xy.

Giúp mik với

 

 

 

 

Answer 1

\(\Leftrightarrow x+y-xy=0\\ \Leftrightarrow\left(y-1\right)-x\left(y-1\right)=-1\\ \Leftrightarrow\left(1-x\right)\left(y-1\right)=-1\\ \Leftrightarrow\left(x-1\right)\left(y-1\right)=1=1.1=\left(-1\right)\left(-1\right)\\ TH_1:\left\{{}\begin{matrix}y-1=1\\x-1=1\end{matrix}\right.\Leftrightarrow x=y=2\\ TH_2:\left\{{}\begin{matrix}x-1=-1\\y-1=-1\end{matrix}\right.\Leftrightarrow x=y=0\)

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