Question

Tìm GTNN của A = |x - 2001| + |x - 1|

Answer 1

\(A\ge\left|x-2001+\left(1-x\right)\right|=\left|-2000\right|=2000\)

GTNN A =2000

khi \(1\le x\le2001\)

Answer 2

\(\left|x-2001\right|+\left|x-1\right|=\left|x-2001\right|+\left|1-x\right|\ge\left|x-2001+1-x\right|=\left|2000\right|=2000\)

\(\text{Dấu "=" xảy ra khi: }\left(1-x\right)\left(x-2001\right)>0\Leftrightarrow1< x< 2001\)

Answer 3

Sửa lại:

\(\left(1-x\right)\left(x-2001\right)\ge0\Leftrightarrow1\le x\le2001\)