Question

 

Tìm tất cả các cặp số nguyên (x;y) thỏa mãn:

xy-3x+y+2=0

Answer 1

xy-3x+y+2=0

=>xy-5x+2x+y+2=0

=>x(y+2)+(y+2)-5x=0

=>(y+2)(x+1)-5x=0

=>(y+2)(x+1)=5x

=>\(\dfrac{x+1}{x}=\dfrac{5}{y+2}\)

\(\Rightarrow\left[{}\begin{matrix}x+1=5\\x=y+2\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=4\\y=2\end{matrix}\right.\)