Question

Gpt: \(|2x-1|+|2x-5|=4\)

Answer 1

Áp dụng BĐT giá trị tuyệt đối ta có:

\(\left|2x-1\right|+\left|2x-5\right|=\left|2x-1\right|+\left|5-2x\right|\ge\left|2x-1+5-2x\right|=\left|4\right|=4\)

Dấu "=" xảy ra khi\(\left(2x-1\right)\left(5-2x\right)\ge0\)

TH1:\(2x-1\le0;5-2x\le0\)

\(\Rightarrow x\le\frac{1}{2};x\ge\frac{5}{2}\)(loại)

TH2:\(2x-1\ge0;5-2x\ge0\)

\(\Rightarrow x\ge\frac{1}{2};x\le\frac{5}{2}\)\(\Leftrightarrow\frac{1}{2}\le x\le\frac{5}{2}\) thoả mãn