Can Mathematica be wrong about the solution of a non-linear system?

Question

I am trying to solve analytically a non-linear system of equations:
Ec1 = A + 2*pvz*Ezmiss - 2*El*Sqrt[Etmiss^2 + Ezmiss^2 + mmiss^2];
Ec2 = B - mmiss^2 + 2*pvz*Ezmiss - 2*Evis*Sqrt[Etmiss^2 + Ezmiss^2 + mmiss^2];
sol = FullSimplify[Solve[Ec1 == 0 && Ec2 == 0, {Ezmiss, mmiss}]]

Mathematica returns four solutions, but I think they are not correct. I have solved the system with SymPy python package and I have also obtained numerical solutions for the system, and both do not coincide with the solution that Mathematica gives me. Am I doing something wrong? Can I simplify things so that Mathematica works better with the system?

Cesareo · Answer

First to facilitate things, make mmiss2 = mmiss^2 and then
Ec1 = A + 2*pvz*Ezmiss - 2*El*Sqrt[Etmiss^2 + Ezmiss^2 + mmiss2];
Ec2 = B - mmiss2 + 2*pvz*Ezmiss - 2*Evis*Sqrt[Etmiss^2 + Ezmiss^2 + mmiss2];
sol = Solve[{Ec1 == 0, Ec2 == 0}, {Ezmiss, mmiss2}, Reals]

The solution is conditional because depending on the values for
{A, B, El, Etmiss, Evis, pvz}

the result could not be real ...

Can Mathematica be wrong about the solution of a non-linear system?

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