Problem 7

Algebra Level 5

\[\frac{H}{K+A}+\frac{K}{H+A}+\frac{A}{H+K}+S\frac{HK+KA+HA}{H^2+K^2+A^2}\geq S+\frac{3}{2}\]

Given that \(H,K,A\) are non-negative. Find the maximum positive real of \(S\).

Give your answer to two decimal places.


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