Question

Tìm GTNN của C = |x - \(\dfrac{2}{5}\)| + |x - \(\dfrac{3}{5}\)|

Answer 1

Giải:

Áp dụng BĐT \(\left|a\right|+\left|b\right|\ge\left|a+b\right|\) ta có:

\(C=\left|x-\dfrac{2}{5}\right|+\left|x-\dfrac{3}{5}\right|=\left|x-\dfrac{2}{5}\right|+\left|\dfrac{3}{5}-x\right|\)

\(\ge\left|x-\dfrac{2}{5}+\dfrac{3}{5}-x\right|=\left|\dfrac{1}{5}\right|=\dfrac{1}{5}\)

Dấu "=" xảy ra \(\Leftrightarrow\hept{\begin{cases}x-\frac{2}{5}\ge0\\\frac{3}{5}-x\ge0\end{cases}}\) \(\Leftrightarrow\dfrac{2}{5}\le x\le\dfrac{3}{5}\)

Vậy \(C_{min}=\dfrac{1}{5}\) \(\Leftrightarrow\dfrac{2}{5}\le x\le\dfrac{3}{5}\)