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Question

Given y2+z2=ayz, z2+x2=bxz, x2+y2=cxy express y2xz+xzy2 in terms of a, b, c.

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Solution

Multiplying 1st and 3rd relations, we get
y2x2+y4+z2x2+z2y2=acy2xz
or (y2x2+y3z2)+(y4+z2x2)=acy2xz
Dividing by y2xz, we get
x2+z2xz+y2xz+xzy2=ac
Substituting x2+z2xz=b from 2nd relation in (1), We get
y2zx+zxy2=acb

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