Ta có :
\(\left|x-2020\right|=\left|2020-x\right|\)
\(\Leftrightarrow\left|x-2019\right|+\left|x-2020\right|=\left|x-2019\right|+\left|2020-x\right|\)
\(\Leftrightarrow A=\left|x-2019\right|+\left|2020-x\right|\ge\left|x-2019+2020-x\right|\)
\(\Leftrightarrow A\ge1\)
Dấu "=" xảy ra
\(\Leftrightarrow\left(x-2019\right)\left(2020-x\right)\le0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-2019\ge0\\2020-x\le0\end{matrix}\right.\\\left\{{}\begin{matrix}x-2019\le0\\2020-x\ge0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge2019\\x\ge2020\end{matrix}\right.\\\left\{{}\begin{matrix}x\le2019\\x\le2020\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow x=2020\)
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