Question

tìm x,y

/x-2015/+/x-2016/+/y-2017/+/x-2018/=3

Answer 1

Áp dụng bđt: \(\left|a\right|+\left|b\right|\ge\left|a+b\right|\) ta có:

\(VT=\left|x-2015\right|+\left|x-2016\right|+\left|y-2017\right|+\left|x-2018\right|\)

\(VT=\left|x-2015\right|+\left|2018-x\right|+\left|x-2016\right|+\left|y-2017\right|\)

\(VT\ge\left|x-2015+2018-x\right|+\left|x-2016\right|+\left|y-2017\right|\)

\(VT\ge3+\left|x-2016\right|+\left|y-2017\right|\ge3\)

\(VT\ge VP\)

Dấu "=" khi: \(\left\{{}\begin{matrix}2015\le x\le2018\\x=2016\\y=2017\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2016\\y=2017\end{matrix}\right.\)