Question

Tìm GTNN

c) \(C=2x+3\sqrt{x}-28\)

d) \(E=\sqrt{\left(x-2011\right)^2+\left(x-1\right)^2}\)

e) \(F=\sqrt{x-2\sqrt{x}-3}\)

Answer 1

\(\left(dk:x\ge0\right)C=2x+3\sqrt{x}-28=2\left(\sqrt{x}+\dfrac{3}{4}\right)^2-\dfrac{233}{8}\ge2\left(\dfrac{3}{4}\right)^2-\dfrac{233}{8}=-28\Rightarrow dấu"="\Leftrightarrow x=0\)

\(d;E=\sqrt{\left(x-2011\right)^2+\left(x-1\right)^2}\Rightarrow\sqrt{2}.E=\sqrt{\left[\left(2011-x\right)^2+\left(x-1\right)^2\right]\left(1+1\right)}\ge2011-1=2010\Rightarrow E\ge\dfrac{2010}{\sqrt{2}}\)

\(dấu"="\Leftrightarrow2011-x=x-1\Leftrightarrow x=1006\)

\(F=\sqrt{x-2\sqrt{x}-3}\ge0\Rightarrow dấu"="\Leftrightarrow x-2\sqrt{x}-3=0\Leftrightarrow x=9\)