# 103 trigonometric problems from

Algebra Level 4

Let $$x,y$$ and $$z$$ be positive numbers satisfying $$x+y+z=xyz$$.

If the maximum value of $$\displaystyle \sum_\text{cyclic} \dfrac x{\sqrt{1+x^2}}$$ can be expressed as $$\dfrac {a\sqrt b}c$$, where $$a,b$$ and $$c$$ are positive integers with $$a,c$$ coprime and $$b$$ square-free, find $$a+b+c$$.

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