Question

Tìm GTNN của biểu thức:

A = |x - 2019| + |x - 2020| + 2

 

Answer 1

 Ta có : \(\left|x-2019\right|\ge x-2019\). Dấu "=" khi \(x-2019\ge0\)

             \(\left|x-2020\right|=\)\(\left|2020-x\right|\ge2020-x\).Dấu "=" khi \(2020-x\ge0\)

=> \(\left|x-2019\right|+\left|2020-x\right|\)\(\ge x-2019+2020-x\)

=> \(\left|x-2019\right|+\left|x-2020\right|+2\)\(\ge3\)

hay \(A\ge3\)

\(MinA=3\Leftrightarrow\)\(\hept{\begin{cases}x-2019\ge0\\2020-x\ge0\end{cases}}\)\(\Leftrightarrow2019\le x\le2020\)