Hmm 5, 12, 13, this seems familiar

Algebra Level 5

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

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

  2. xy+yz+zx=1xy+yz+zx = 1

Anqi Li by Anqi Li
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