MathDB
2022 W CHMMC Tiebreaker 3 - max |-a^6+b^6+c^6|, complex

Source:

March 2, 2024
algebracomplex numbersinequalitiesCHMMC

Problem Statement

Suppose that a,b,ca,b,c are complex numbers with a+b+c=0a+b+c = 0, ∣abc∣=1|abc| = 1, ∣b∣=∣c∣|b| = |c|, and 9−3348≤cos⁡2(arg(ba))≤9+3348.\frac{9-\sqrt{33}}{48} \le \cos^2 \left( arg \left( \frac{b}{a} \right) \right)\le \frac{9+\sqrt{33}}{48} . Find the maximum possible value of ∣−a6+b6+c6∣|-a^6+b^6+c^6|.
Back to ProblemsView on AoPS