2 Mathematicians creating Madness

Algebra Level 5

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

a2+b2+c2=66a^{2} + b^{2} +c^{2} = 66 a3+b3+c3=408a^{3} + b^{3} + c^{3} = 408a4+b4+c4=2658a^{4} + b^{4} + c^{4} = 2658 This is part of Ordered Disorder.

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