Question

GTNN của \(\left|x-1,5\right|+\left|x-2,5\right|\)

Answer 1

\(A=\left|x-1,5\right|+\left|x-2,5\right|\)

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

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

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

Dấu "=" xảy ra khi \(1,5\le x\le2,5\)

Vậy \(Min_A=1\) khi \(1,5\le x\le2,5\)

Answer 2

Đặt \(A=\left|x-1,5\right|+\left|x-2,5\right|=\left|x-1,5\right|+\left|2,5-x\right|\)

Ta có: \(A\ge\left|x-1,5+2,5-x\right|=1\)

Dấu " = " xảy ra khi \(x-1,5\ge0;2,5-x\ge0\)

\(\Rightarrow x\ge1,5;x\le2,5\)

\(\Rightarrow1,5\le x\le2,5\)

Vậy \(MIN_A=1\) khi \(1,5\le x\le2,5\)