Question

Tìm giá trị nhỏ nhất của:

A = \(\left|x-2015\right|\) + \(\left|x-2016\right|+\left|x-2017\right|\)

Answer 1

\(A=\left|x-2015\right|+\left|x-2016\right|+\left|x-2017\right|\)

\(A=\left|x-2015\right|+\left|x-2017\right|+\left|x-2016\right|\)

\(A=\left|x-2015\right|+\left|2017-x\right|+\left|x-2016\right|\)

\(A\ge\left|x-2015+2017-x\right|+\left|x-2016\right|\)

\(A\ge2+\left|x-2016\right|\)

Vì \(\left|x-2016\right|\ge0\forall x\in R\) nên

\(A\ge2\)

Dấu "=" xảy ra khi: \(\left\{{}\begin{matrix}x-2015\ge0\\x-2016=0\\x-2017\le0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge2015\\x=2016\\x\le2017\end{matrix}\right.\Leftrightarrow x=2016\)