Calculating the bi-tangents of x4+y3+1=0x^4+y^3+1=0

Algebra Level 5

For how many ordered pairs of complex numbers (a,b)(a,b) is the polynomial P(x)=x4+(ax+b)3+1P(x)=x^4+(ax+b)^3+1 equal to a square of a complex polynomial?

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