MathDB

system of equations

Source: bmo 1984

April 23, 2007

algebra proposedalgebra

Problem Statement

Let

a,b,c

be positive real numbers. Find all real solutions

(x,y,z)

of the system:

ax+by=(x-y)^{2} \\ by+cz=(y-z)^{2} \\ cz+ax=(z-x)^{2}