Geometry in inequality
Geometry
Level
5
\[\large{ \dfrac{2}{\sqrt{a^2+1}} + \dfrac{1}{\sqrt{b^2+1}} + \dfrac{1}{\sqrt{c^2+1}} }\]
Suppose \(a,b,c\) are positive real numbers satisfying \(a+b+c = abc\). Let \(P\) be the maximum value of the above expression. Find the value of \(\left\lfloor 10000P \right\rfloor\).
Clarification: The numerator of the first fraction is indeed 2.
by
MS HT