4xyz = a^2x + b^2y + c^2z + abc
Source: IMO Shortlist 1995, A4, , Titu Andreescu
March 26, 2005
functioninequalitiesIMO Shortlistoptimizationsystem of equations133109
Problem Statement
Find all of the positive real numbers like such that :
1.) x \plus{} y \plus{} z \equal{} a \plus{} b \plus{} c
2.) 4xyz \equal{} a^2x \plus{} b^2y \plus{} c^2z \plus{} abc
Proposed to Gazeta Matematica in the 80s by VASILE CÎRTOAJE and then by Titu Andreescu to IMO 1995.