Question

tìm các cặp số nguyên (x,y) thỏa mãn phương trình sau : x² - y²= 2017

Answer 1

\(\Leftrightarrow\left(x-y\right)\left(x+y\right)=2017=1.2017\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-y=1\\x+y=2017\end{matrix}\right.\\\left\{{}\begin{matrix}x-y=-1\\x+y=-2017\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=1009\\y=1008\end{matrix}\right.\\\left\{{}\begin{matrix}x=-1009\\y=-1008\end{matrix}\right.\end{matrix}\right.\)