Question

tìm GTNN của A= \(\dfrac{\sqrt{x}}{\sqrt{x}+3}\)

Answer 1

\(A=\dfrac{\sqrt{x}}{\sqrt{x}+3}=\dfrac{\sqrt{x}+3-3}{\sqrt{x}+3}=1-\dfrac{3}{\sqrt{x}+3}\ge1-\dfrac{3}{3}=1-1=0\)

Vậy GTNN của A là 0 khi \(x=0\)

Answer 2

\(A=\dfrac{\sqrt{x}}{\sqrt{x}+3}=\dfrac{\sqrt{x}+3}{\sqrt{x}+3}+\dfrac{-3}{\sqrt{x}+3}\\ A=1+\dfrac{-3}{\sqrt{x}+3}\)

Vì \(\sqrt{x}+3\ge3\Rightarrow\dfrac{-3}{\sqrt{x}+3}\ge\left(-1\right)\)

\(\Rightarrow A=1+\dfrac{-3}{\sqrt{x}+3}\ge0\)

Vậy Amax=0 khi x=0