HMMT 2025 A10

Let $a$ , $b$ , and $c$ be pairwise distinct complex numbers such that

$a^{2} = b + 6, b^{2} = c + 6, \mathrm{and} c^{2} = a + 6.$

Compute the two possible values of $a + b + c$

Dataset text NuminaMath olympiads. Quoted with source.

Solutions

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