Two Equal Cubes

Problem

Prove that for all real numbers $a, b, c$ ,

\left((2a-b-c) + (b-c)\sqrt{3}\,\mathrm{i}\right)^3 = \left((2b-c-a) + (c-a)\sqrt{3}\,\mathrm{i}\right)^3.

Answer

Solution

Difficulty	4/10
Topics	complex numbers, algebra, Symmetry

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