Question

[PHẠM THỊ THIÊN HUẾ]

\(GTNN:\sqrt{x^2+2x+5}\)

\(GTNN:\sqrt{4x^2-4x+1}+\sqrt{4x^2-12x+9}\)giúp mik với!!!

Answer 1

[Thắng Nguyễn]

Bài 1: \(\sqrt{x^2+2x+5}=\sqrt{\left(x^2+2x+1\right)+4}\)

\(=\sqrt{\left(x+1\right)^2+4}\ge\sqrt{4}=2\)

Dấu "=" xảy ra khi \(x=-1\)

Vậy...

Bài 2:

\(\sqrt{4x^2-4x+1}+\sqrt{4x^2-12x+9}\)

\(=\sqrt{\left(2x-1\right)^2}+\sqrt{\left(2x-3\right)^2}\)

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

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

Dấu "=" xảy ra khi \(\frac{1}{2}\le x\le\frac{3}{2}\)

Vạy....