What convex function should be used here?
Algebra
Level
3
\[\dfrac{1}{\sqrt{a^3+1}}+\dfrac{1}{\sqrt{b^3+1}}+\dfrac{1}{\sqrt{c^3+1}}. \]
Positive reals \(a,\ b,\ c\) satisfy \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=3.\)
If the maximum value of the above expression is in the form \(\dfrac{x}{\sqrt y}\), where \(x\) and \(y\) are integers with \(y\) square-free, find \(x+y\).
by
Rohit Udaiwal