2005 OIM Problems/Problem 1
Problem
Determine all triples of real numbers 
that satisfy the following system of equations:
![\[xyz = 8\]](http://latex.artofproblemsolving.com/9/4/f/94f7d6eaab85dca74ec09823d71f9d01485cc623.png)
![\[x^2y+y^2z+z^2x=73\]](http://latex.artofproblemsolving.com/a/6/0/a603f9ca3845c04dd25ec03bed61ea25cd3467b3.png)
![\[x(y-z)^2+y(z-x)^2+z(x-y)^2=98\]](http://latex.artofproblemsolving.com/f/4/c/f4c137f69052b5890bdc94a4230339d21db36906.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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