A Nice Algebra Problem | America Math Olympiad

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[@thomazsoares1316]

S = {-1 ; ³√2}

[@MrGeorge1896]

with x³ = 2 and x³ = -1 as the two trivial solutions:
x³ - 2 = 0 = (x - ∛2) (x² + (∛2)x + ∛4) and x³ + 1 = 0 = (x + 1) (x² - x + 1)
so we get x⁶ - x³ - 2 = 0 = (x - ∛2) (x² + (∛2)x + ∛4) (x + 1) (x² - x + 1) with two real and four complex solutions.

[@MathematicsAlgebra-go5ih]

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