Đặt \(A=\left|x-2018\right|+\left|x-2020\right|\)
\(\ge\left|\left(x-2018\right)+\left(2020-x\right)\right|=2\)
(Dấu "="\(\Leftrightarrow\left(x-2018\right)\left(2020-x\right)\ge0\)
\(\Leftrightarrow2018\le x\le2020\))
Vậy \(A_{min}=2\Leftrightarrow2018\le x\le2020\)
Đặt \(B=\left|x-2019\right|\ge0\)
(Dấu "="\(\Leftrightarrow x-2019=0\Leftrightarrow x=2019\))
Vậy \(B_{min}=0\Leftrightarrow x=2019\)
\(\Rightarrow\left|x-2018\right|+\left|x-2019\right|+\left|x-2020\right|\ge2\)
(Dấu "="\(\Leftrightarrow\hept{\begin{cases}2018\le x\le2020\\x=2019\end{cases}}\Leftrightarrow x=2019\))
Vậy \(BT_{min}=2\Leftrightarrow x=2019\)
