2005 OIM Problems/Problem 1

Problem

Determine all triples of real numbers $(x, y, z)$ that satisfy the following system of equations:

\[xyz = 8\] \[x^2y+y^2z+z^2x=73\] \[x(y-z)^2+y(z-x)^2+z(x-y)^2=98\]

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions