Question

tìm các cặp số nguyên dương (x;y) thỏa mãn phương trình sau: 4x+11y=4xy

Answer 1

Ta có \(4x+11y=4xy\Leftrightarrow4xy-4x-11y+11=11\Leftrightarrow4x\left(y-1\right)-11\left(y-1\right)=11\Leftrightarrow\left(y-1\right)\left(4x-11\right)=11\Leftrightarrow\)\(\left[{}\begin{matrix}\left\{{}\begin{matrix}y-1=1\\4x-11=11\end{matrix}\right.\\\left\{{}\begin{matrix}y-1=11\\4x-11=1\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\)\(\left[{}\begin{matrix}\left\{{}\begin{matrix}y=2\\x=\dfrac{11}{2}\end{matrix}\right.\\\left\{{}\begin{matrix}y=12\\x=3\end{matrix}\right.\end{matrix}\right.\)

Vì x,y nguyên dương

Vậy (x;y)=(3;12)