\(A=\left|x-2017\right|+\left|x-2018\right|=\left|x-2017\right|+\left|2018-x\right|\ge\left|x-2017+2018-x\right|=1\)
Dấu "=" xảy ra \(\Leftrightarrow\left(x-2017\right)\left(2018-x\right)\ge0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-2017\ge0\\2018-x\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}x-2017\le0\\2018-x\le0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge2017\\2018\ge x\end{matrix}\right.\\\left\{{}\begin{matrix}2018\le x\\x\le2017\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}2017\le x\le2018\\x\in\varnothing\end{matrix}\right.\)
Vậy ...
|A|+|B|\(\ge\)|A+B|
Ta có:
|x - 2017| + |x - 2018|
=|x-2017|+|2018-x|
\(\ge\)|x-2017+2018-x|=1
Dấu "=" xảy ra khi (x-2017)(x-2018)\(\ge\)0\(\Rightarrow\)2017\(\le\)x\(\le\)2018
