Question

Tìm GTNN của Q=/x-3/+/x+1/+/x+2/

Answer 1

Lỗi r .

Answer 2

- Tìm GTNN của Q=\(\left|x-3\right|+\left|x+1\right|+\left|x+2\right|\) :)

Answer 3

\(Q=\left|x-3\right|+\left|x+1\right|+\left|x+2\right|\)

\(\Rightarrow Q=\left(\left|3-x\right|+\left|x+2\right|\right)+\left|x+1\right|\)

\(\Rightarrow Q\ge\left|3-x+x+2\right|+\left|x+1\right|\)

\(\Rightarrow Q\ge5+\left|x+1\right|\ge5\)

Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}\left(x-3\right)\left(x+2\right)\ge0\\\left|x+1\right|=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}-2\le x\le3\\x=-1\end{matrix}\right.\)\(\Leftrightarrow x=-1\)

Vậy \(Q_{min}=5\Leftrightarrow x=-1\)