Question

Tìm GTNN của

\(A=x-\sqrt{x}\)

\(B=x-\sqrt{x-2005}\)

Giúp mình vs ạ 

Answer 1

\(A=\left(x-\sqrt{x}+\frac{1}{4}\right)-\frac{1}{4}\)

\(A=\left(\sqrt{x}-\frac{1}{2}\right)^2-\frac{1}{4}\ge\frac{-1}{4}\)Dấu "=" xảy ra khi \(\sqrt{x}=\frac{1}{2}\Leftrightarrow x=\frac{1}{4}\)

\(B=\left(\left(x-2005\right)-\sqrt{x-2005}+\frac{1}{4}\right)+\frac{8019}{4}\)

\(B=\left(\sqrt{x=2005}-\frac{1}{2}\right)^2+\frac{8019}{4}\ge\frac{8019}{4}\)

Dấu "=" xảy ra khi \(\sqrt{x-2005}=\frac{1}{2}\Rightarrow x-2005=\frac{1}{4}\Leftrightarrow x=\frac{8021}{4}\)