How do you prove that for all positive $a,b,c$ this formula holds true:
\begin{equation*} \frac{a}{\sqrt{a+b}} + \frac{b}{\sqrt{b+c}} + \frac{c}{\sqrt{c+a}} > \sqrt{a+b+c}? \end{equation*}
Any help will be invaluable.
How do you prove that for all positive $a,b,c$ this formula holds true:
\begin{equation*} \frac{a}{\sqrt{a+b}} + \frac{b}{\sqrt{b+c}} + \frac{c}{\sqrt{c+a}} > \sqrt{a+b+c}? \end{equation*}
Any help will be invaluable.