Prove that a + b + c = 0
Source: JBMO 1999, Problem 1
October 30, 2005
algorithm
Problem Statement
Let be five real numbers such that a^3 \plus{} ax \plus{} y \equal{} 0, b^3 \plus{} bx \plus{} y \equal{} 0 and c^3 \plus{} cx \plus{} y \equal{} 0. If are all distinct numbers prove that their sum is zero.
Ciprus