Question

Tìm cặp số x,y nguyên biết:

\(\left|x-2y-1\right|=\dfrac{10}{\left|y-4\right|+2}\)

@ Mashiro Shiina

@Akai Haruma

@Nguyễn Thanh Hằng

Answer 1

Với mọi x,y ta có :

\(+,\left|x-2y-1\right|\ge0\)

+, \(\left|y-4\right|+2\ge2\Leftrightarrow\dfrac{10}{\left|x-4\right|+2}\le5\)

Dấu "=" xảy ra khi :

\(\left\{{}\begin{matrix}\left|x-2y-1\right|=5\\\dfrac{10}{\left|x-4\right|+2}=5\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}y=4\\x=9\end{matrix}\right.\)

Vậy ..