Question

Tìm các số nguyên (x;y) thỏa mãn |x-5|+|x-1| = 12/|y+5|+3

nhanh nha!

Answer 1

\(\left|x-5\right|+\left|x-1\right|=\dfrac{12}{\left|y+5\right|+3}\)

Ta có:\(\left\{{}\begin{matrix}\left|x-5\right|+\left|x-1\right|=\left|5-x\right|+\left|x-1\right|\ge\left|5-x+x-1\right|=4\\\dfrac{12}{\left|y+5\right|+3}\le\dfrac{12}{3}=4\end{matrix}\right.\)

Nên \(\left|x-5\right|+\left|x-1\right|=\dfrac{12}{\left|y+5\right|+3}=4\)

\(\Rightarrow\left\{{}\begin{matrix}1\le x\le5\\y=-5\end{matrix}\right.\)