199 upvotes problem
Algebra
Level
4
\[\large \dfrac{1}{a^{2}+9} + \dfrac{1}{b^{2}+9} + \dfrac{1}{c^{2}+9} \]
Given that \(a,b\) and \(c\) are positive reals with a sum of 1. If the maximum value of the above expression can be expressed as \(\dfrac{x}{y}\) where \(x\) and \(y\) are coprime integers, find the value of \(x+y\).
by
Surya Prakash