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x^3 +y^3 +k(x^2 +y^2) = y^3 +z^3 +k(y^2 +z^2) = ...=2008

Source: JBMO 2008 Shortlist A1

October 14, 2017
JBMOalgebra

Problem Statement

If for the real numbers x,y,z,kx, y,z, k the following conditions are valid, x≠y≠z≠xx \ne y \ne z \ne x and x3+y3+k(x2+y2)=y3+z3+k(y2+z2)=z3+x3+k(z2+x2)=2008x^3 +y^3 +k(x^2 +y^2) = y^3 +z^3 +k(y^2 +z^2) = z^3 +x^3 +k(z^2 +x^2) = 2008, fi nd the product xyzxyz.
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