One-rooted Polynomials

Algebra Level 5

For how many ordered triples of complex numbers (a,b,c)(a,b, c), do we have

x3a2x2+(32ab)x+(5b2)=(x+c)3?x^3-a^2x^2+(3-2ab)x+(5-b^2) = (x+c)^3?

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