Question

tìm cặp số (x,y) thuộc N sao cho :

xy - 5x -3y + 8=0

Answer 1

xy-5x-3y+8=0

x(y-5)-3(y-5)=7

(y-5)(x-3)=7

\(\Rightarrow y-5;x-3\inƯ\left(7\right)=\left\{1;-1;7;-7\right\}\)

\(\left[{}\begin{matrix}\left\{{}\begin{matrix}y-5=1\\x-3=7\end{matrix}\right.\\\left\{{}\begin{matrix}y-5=7\\x-3=1\end{matrix}\right.\\\left\{{}\begin{matrix}y-5=-1\\x-3=-7\end{matrix}\right.\\\left\{{}\begin{matrix}y-5=-7\\x-3=-1\end{matrix}\right.\end{matrix}\right.\)

\(\left[{}\begin{matrix}\left\{{}\begin{matrix}y=6\\x=10\end{matrix}\right.\\\left\{{}\begin{matrix}y=10\\x=6\end{matrix}\right.\\\left\{{}\begin{matrix}y=4\\x=-4\end{matrix}\right.\\\left\{{}\begin{matrix}y=-4\\x=4\end{matrix}\right.\end{matrix}\right.\)