Ta có :
\(B=\left|5x-200\right|+\left|5x+1\right|=\left|200-5x\right|+\left|5x+1\right|\)
Với \(\forall x\) ta có :
\(B=\left|200-5x\right|+\left|5x+1\right|\)
\(\Leftrightarrow B\ge\left|200-5x+5x+1\right|\)
\(\Leftrightarrow B\ge\left|199\right|\)
\(\Leftrightarrow B\ge199\)
Dấu "=" xảy ra khi và chỉ khi :
\(\left(200-5x\right)\left(5x+1\right)\ge0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}200-5x\ge0\\5x+1\ge0\end{matrix}\right.\\\left\{{}\begin{matrix}200-5x\le0\\5x+1\le0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x\le40\\x\ge-\dfrac{1}{5}\end{matrix}\right.\\\left\{{}\begin{matrix}x\ge40\\x\le-\dfrac{1}{5}\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}40\ge x\ge-\dfrac{1}{5}\\x\in\varnothing\end{matrix}\right.\)
Vậy ...
