Problem 42

Algebra Level 5

$\large a\sqrt{8}+b\sqrt{6}+c\sqrt{2}\geq k\sqrt{a^2+b^2+c^2}$

Given that $$a,b$$ and $$c$$ are the lengths of the right triangle $$ABC$$. Find the maximum value of $$k$$ that satisfies the inequality above.

Set.

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