# Decimate the decimals

Algebra Level 4

Let $x,y,z$ be positive numbers such that $x+y+z=2$ and $xy+yz+zx=1$. Given that $\large x^{20.17}+y^{20.17}+z^{20.17}$ achieves its maximum value when $(x,y,z)=(X,Y,Z)$, and that $XYZ=\frac{a}{b},$ where $a$ and $b$ are coprime positive integers, find $a+b$.

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