\(B=x-\sqrt{x-2005}\left(x\ge2005\right)\)
\(\Rightarrow B=\left(x-2005\right)-\sqrt{x-2005}+2005\)
Đặt \(t=\sqrt{x-2005}\ge0\)
\(\Rightarrow B=t^2-t+2005=t^2-t+\dfrac{1}{4}-\dfrac{1}{4}+2005\)
\(\Rightarrow B=\left(t-\dfrac{1}{2}\right)^2+\dfrac{8019}{4}\ge\dfrac{8019}{4}\)
Vậy \(GTNN\left(B\right)=\dfrac{8019}{4}\)
Dấu '=' xảy ra khi \(t=\dfrac{1}{2}\Leftrightarrow\sqrt{x-2005}=\dfrac{1}{2}\)
\(\Leftrightarrow2x-8020=1\)
\(\Leftrightarrow x=\dfrac{8021}{2}\)
\(B=x-2005-\sqrt{x-2005}+2005=\left(\sqrt{x-2005}-\dfrac{1}{2}\right)^2+\dfrac{8019}{4}\ge\dfrac{8019}{4}\)
\(B_{min}=\dfrac{8019}{4}\) khi \(\sqrt{x-2005}=\dfrac{1}{2}\Rightarrow x=\dfrac{8021}{4}\)
