Question

Tìm GTNN của A=\(\left|2x+\dfrac{1}{2}\right|+\left|\dfrac{3}{2}-2x\right|\)

Answer 1

Áp dụng bất đẳng thức \(\left|A\right|+\left|B\right|\ge\left|A+B\right|\) vào biểu thức A có:

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

Dấu"=" xảy ra \(\Leftrightarrow\left(2x+\dfrac{1}{2}\right)\left(\dfrac{3}{2}-2x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+\dfrac{1}{2}=0\\\dfrac{3}{2}-2x=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{4}\\x=\dfrac{3}{4}\end{matrix}\right.\)

Vậy MinA=2 \(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{4}\\x=\dfrac{3}{4}\end{matrix}\right.\)