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Use NSolve for a system of two nonlinear equations two unknowns?

Posted 25 days ago
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Dear Fellows,

I used NSolve to solve a nonlinear system of two equations with two unknowns as follows:

NSolve[{-2.9*(10^(-15))*(y-x)^2+x^2*(y-x)^2-x^4==0,-2.9*(10^(-15))*(y-x)^2+(y-x)^2*y^2+y^4==0},{x,y},20]

I expect to receive just 4 solutions for this system of equations. However, mathematica provides a lot of solutions including 4 real and 4 complex solutions. I can reproduce the real solutions (almost similar) with FindRoot command of Mathematica. Would some body plz hint me how these complex solutions are found? Isn't NSolve supposed to return only 4 solutions for a fourth order equation totally?

2 Replies

they're fourth order in two variables

Bezout's theorem allows for as many as 4*4 = 16 solutions (product of total degrees). So 14, which is what I see in version 11.3, is certainly plausible.

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