Ta có: B = |x-2020|+|x-1|
⇒ |x-2020|+|1-x| ≥ |x -2020+1-x|
⇒ |x-2020|+|x-1| ≥ 1
Dấu bằng xảy ra khi: (x-2020)×(x-1)≥0
TH1: \(\left[ \begin{array}{l}x-2018<0\\1-x<0\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x<2018\\x>1\end{array} \right.\)
TH1: \(\left[ \begin{array}{l}x-2018>0\\1-x>0\end{array} \right.\)
⇒ \(\left[ \begin{array}{l}x>2018\\x<1\end{array} \right.\)
⇒2018>x>1
Vậy GTNN của B = 1 với 2018>x>1
