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8(x+1/x) =15(y+1/y) = 17(z+1/z), xy + yz + zx=1

Source: Mathcenter Contest / Oly - Thai Forum 2009 R2 p4 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 9, 2022
algebrasystem of equationsSystem

Problem Statement

Find the values of the real numbers x,y,zx,y,z that correspond to the system of equations. 8(x+1x)=15(y+1y)=17(z+1z)8(x+\frac{1}{x}) =15(y+\frac{1}{y}) = 17(z+\frac{1}{z}) xy+yz+zx=1xy + yz + zx=1 (Heir of Ramanujan)
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