2 Mathematicians creating Madness

Algebra Level 5

How many ordered triples of real numbers \( (a, b, c) \) are there which satisfy:

\[a^{2} + b^{2} +c^{2} = 66\] \[a^{3} + b^{3} + c^{3} = 408\]\[a^{4} + b^{4} + c^{4} = 2658\] This is part of Ordered Disorder.

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