Question

Ta có  \(\left|3x-1\right|+\left|5-3x\right|\) ≥ 4

Tìm dấu "=" xẩy ra ?

Giúp mình với

Answer 1

|3x-1|+|5-3x|≥|3x-1+5-3x|=4

Dấu ''='' ⇔(3x-1)(5-3x)≥0

⇒\(\dfrac{1}{3}\)≤x≤\(\dfrac{5}{3}\)

Answer 2

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

\(\Rightarrow\left|3x-1\right|+\left|5-3x\right|\ge\left|3x-1+5-3x\right|=\left|4\right|=4\)

Dấu \("="\Leftrightarrow\left(3x-1\right)\left(5-3x\right)\ge0\Leftrightarrow\dfrac{1}{3}\le x\le\dfrac{5}{3}\)