MathDB

4

Part of 2015 Czech and Slovak Olympiad III A

Problems(1)

Unhomogenous system of equations

Source: Czech and Slovak Olympiad 2015, National Round, Problem 4

4/1/2015
Find all real triples (a,b,c)(a,b,c), for which a(b2+c)=c(c+ab)a(b^2+c)=c(c+ab) b(c2+a)=a(a+bc)b(c^2+a)=a(a+bc) c(a2+b)=b(b+ca).c(a^2+b)=b(b+ca).
algebrasystem of equations