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Question: Solve System of 2 variables

Question:Solve System of 2 variables

digerdiga 385 Maple 17
gsolve
July 31 2013
1

Hello I have the following system of equations and I want to solve for rho1 and z1

E := (1/2)*(1/rho1^2+1/rho1^2)-1/sqrt(z1^2+rho1^2)-1/sqrt((R-z1)^2+rho1^2)-1/sqrt(z1^2+rho1^2)-1/sqrt((R-z1)^2+rho1^2)+1/R+1/sqrt((2*rho1)^2+(R-2*z1)^2);

Er1 := diff(E, rho1);

Ez1 := diff(E, z1);

solve([Er1, Ez1], {z1, rho1});

The system is a function of R.

The solve command spits out Kernel lost after some time. So my question is how can I solve it ?

When I have some complicated equation and I want to solve for it with 1 parameter (in this case R) then I can at least use RootOf.

But I cannot use RootOf as numeric solution for a system right?

What possibilities do I have?

Is Groebner here any help?
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