# Hmm 5, 12, 13, this seems familiar

Algebra Level 5

Find the sum of $x$ of all possible values of triples of positive real values $(x,y,z)$ such that:

1. $5( x+ \frac{1}{x}) = 12(y + \frac{1}{y}) = 13(z+ \frac{1}{z})$

2. $xy+yz+zx = 1$

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