\(A=\left|x-2019\right|+\left|x-2020\right|\)
\(=\left|x+\left(-2019\right)\right|+\left|2020-x\right|\)
Ta có :
\(\left\{{}\begin{matrix}\left|x+\left(-2019\right)\right|\ge x+\left(-2019\right)\\\left|2020-x\right|\ge2020-x\end{matrix}\right.\)\(=>A\ge x+\left(-2019\right)+2020-x\)
=>\(A\ge1\)
Dấu "=" xảy ra khi
\(\left\{{}\begin{matrix}x+\left(-2019\right)\ge0\\2020-x\ge0\end{matrix}\right.\)\(=>2019\le x\le2020\)
Vậy GTNN của A=1
Khi \(2019\le x\le2020\)
\(A=\left|x-2019\right|+\left|x-2020\right|\)
\(A=\left|2019-x\right|+\left|x-2020\right|\ge\left|2019-x+x-2020\right|=\left|-1\right|=1\)
\(\Rightarrow A\ge1\)
Dấu '' = '' xảy ra
\(\)\(\Leftrightarrow\left\{{}\begin{matrix}2019-x\ge0\\x-2020\ge0\end{matrix}\right.\)
\(\Leftrightarrow2019\le x\le2020\)
Vậy Min A = 1 \(\Leftrightarrow2019\le x\le2020\)