Question

Tìm Min của: a)B=\(\left|3x-7\right|-\left|3x+2\right|+8\)

b)C=\(\left|X+2\right|+\left|2X+5\right|+\left|X-3\right|\)

Answer 1

\(B=\left|3x-7\right|-\left|3x+2\right|+8\)

Áp dụng tính chất:

\(\left|x\right|-\left|y\right|\le\left|x-y\right|\)

\(\left|3x-7\right|-\left|3x+2\right|\le\left|3x-7-3x-2\right|\)

\(B\le9+8=17\)

Dấu "=" xảy ra khi:

\(\left[{}\begin{matrix}\left\{{}\begin{matrix}3x-7\ge0\Rightarrow3x\ge7\Rightarrow x\ge\dfrac{7}{3}\\3x+2\ge0\Rightarrow3x\ge-2\Rightarrow x\ge\dfrac{-2}{3}\end{matrix}\right.\\\left\{{}\begin{matrix}3x-7< 0\Rightarrow3x< 7\Rightarrow x< \dfrac{7}{3}\\3x+2< 0\Rightarrow3x< -2\Rightarrow x< -\dfrac{2}{3}\end{matrix}\right.\end{matrix}\right.\)

Vậy \(x\ge\dfrac{7}{3}\) hoặc \(x< -\dfrac{2}{3}\)