Question

Tìm GTLN của: \(A=\dfrac{\sqrt{x}+1}{2\sqrt{x}+1}\)

Answer 1

\(A=\dfrac{2\sqrt{x}+1-\sqrt{x}}{2\sqrt{x}+1}=1-\dfrac{\sqrt{x}}{2\sqrt{x}+1}\)

Do \(\left\{{}\begin{matrix}\sqrt{x}\ge0\\2\sqrt{x}+1>0\end{matrix}\right.\) \(\Rightarrow\dfrac{\sqrt{x}}{2\sqrt{x}+1}\ge0\)

\(\Rightarrow A\le1\)

\(A_{max}=1\) khi \(x=0\)