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:
\( 5( x+ \frac{1}{x}) = 12(y + \frac{1}{y}) = 13(z+ \frac{1}{z}) \)
\(xy+yz+zx = 1 \)
by
Anqi Li