MathDB
Romania District Olympiad 2001 - Grade X

Source:

March 16, 2011
algebra proposedalgebra

Problem Statement

Two numbers (z1,z2)∈C∗×C∗(z_1,z_2)\in \mathbb{C}^*\times \mathbb{C}^* have the property (P)(P) if there is a real number a∈[−2,2]a\in [-2,2] such that z12−az1z2+z22=0z_1^2-az_1z_2+z_2^2=0. Prove that if (z1,z2)(z_1,z_2) have the property (P)(P), then (z1n,z2n)(z_1^n,z_2^n) satisfy this property, for any positive integer nn.
Dorin Andrica
Back to ProblemsView on AoPS