An algebra problem by Amar Mavi

Algebra Level 4

$\large \dfrac a{\sqrt{8a^2 + bc}} + \dfrac b{\sqrt{8b^2 + ac}} + \dfrac c{\sqrt{8c^2 + ab}}$

If $$a,b$$ and $$c$$ are positive reals, find the maximum value of the expression above.

Give your answer to 3 decimal places.

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