\(D=\left|x-2019\right|+\left|x-2020\right|\)
Ta có: \(\left|x-2020\right|=\left|2020-x\right|\)
\(\Rightarrow\left|x-2019\right|+\left|x-2020\right|=\left|x-2019\right|+\left|2020-x\right|\)
\(\Rightarrow D=\left|x-2019\right|+\left|2020-x\right|\ge\left|x-2019+2020-x\right|\)
\(\Rightarrow D\ge1\)
Dấu " = " xảy ra khi và chỉ khi:
\(\left(x-2019\right)\left(2020-9\right)\le0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-2019\ge0\\2020-9\le0\end{matrix}\right.\\\left\{{}\begin{matrix}x-2019\le0\\2020-x\ge0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\ge2019\\x\ge2020\end{matrix}\right.\\\left\{{}\begin{matrix}x\le2029\\x\le2020\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow x=2020\)
Vậy ................
