You can start by trying FindRoot
eq1 = Sqrt[(-19.4 + x)^2 + (20.8 + y)^2 + (-11.4 + z)^2] + Sqrt[x^2 + y^2 + z^2] == -10.496;
eq2 = Sqrt[(-16.5 + x)^2 + (29.2 + y)^2 + (-6.7 + z)^2] + Sqrt[x^2 + y^2 + z^2] == -8.382;
eq3 = Sqrt[(-17.6 + x)^2 + (33.2 + y)^2 + (1.3 + z)^2] + Sqrt[x^2 + y^2 + z^2] == -8.938;
FindRoot[{eq1, eq2, eq3}, {x, 1}, {y, 1}, {z, 1}]
{x -> 5.46311, y -> -2.52191, z -> -0.822461}
If you can setup your system as Ax=b
, you can also try LinearSolve
which obtain least squares approximation of solution. But your equations are not linear, so this would not work in this case. There might be other methods, but if NSolve fails, that is what I try next (btw, use the Reals
option with NSolve
and Solve
helps sometimes finding a solution, but not in this case). May be someone else will have better answer for you.