# Problem 19

Algebra Level 5

$\large x^5+y^5+z^5$

Given that $$x,y$$ and $$z$$ are real numbers satisfying $$x+y+z=0$$ and $$x^2+y^2+z^2 = 1$$. And the maximum value of of the expression above can be expressed as $$\dfrac{ H\sqrt K}A$$, where $$A,H$$ and $$K$$ are positive integers with $$K$$ square-free and $$A,H$$ copime. Find $$H+K+A$$.

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