proving the independance of an equation, from certain variables

by kenith   Last Updated April 15, 2019 10:20 AM

The different and unequal to zero real numbers x, y, z satisfy the equation

$x^3+y^3+m(x+y)=y^3+z^3+m(y+z)=z^3+x^3+m(z+x)$

prove that

$K=(\frac{x-y}{z}$ $+\frac{y-z}{x}$ $+\frac{z-x}{y})$ $(\frac{z}{x-y}$ $+\frac{x}{y-z}$ $+\frac{y}{z-x})$ is not dependnent upon $x, y, z, m$

I don't know how to solve the question above. I've been trying it for a while, but I can't. Can you guys please help me?

Thanking you in advance

Kevin



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