Question

Tính giá trị lớn nhất

\(A=\frac{\sqrt{x-2013}}{x+2}+\frac{\sqrt{x-2014}}{x}\)

Answer 1

ĐK : \(\hept{\begin{cases}x\ge2013\\y\ge2014\end{cases}}\)

Ta có \(A=\frac{\sqrt{\left(x-2013\right).2015}}{\sqrt{2015}\left(x+2\right)}+\frac{\sqrt{\left(x-2014\right).2014}}{\sqrt{2014}.x}\le\frac{\frac{x-2013+2015}{2}}{\sqrt{2015}\left(x+2\right)}+\frac{\frac{x-2014+2014}{2}}{\sqrt{2014}.x}\)

\(\Rightarrow A\le\frac{1}{2\sqrt{2015}}+\frac{1}{2\sqrt{2014}}\)

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