# Solving system of equations with Summation

I have these three equations (eq1, eq2, eq3):

Clear["Global*"]
r[i]=Sqrt[(x[i]-a)^2+(y[i]-b)^2+(z[i]-c)^2];
eq1=(1/m)Sum[x[i],{i,1,m}]+(1/(m^2))Sum[r[i],{i,1,m}]Sum[(a-x[i])/r[i],
{i,1,m}]-a;
eq2=(1/m)Sum[y[i],{i,1,m}]+(1/(m^2))Sum[r[i],{i,1,m}]Sum[(b-y[i])/r[i],
{i,1,m}]-b;
eq3=(1/m)Sum[z[i],{i,1,m}]+(1/(m^2))Sum[r[i],{i,1,m}]Sum[(c-z[i])/r[i],
{i,1,m}]-c;


I want to solve them for (a,b,c) making eq1, eq2 and eq3 equal to zero. I saw this technique but I can't make it work for a system of equations. Can it be done for an arbitrary value of m?

• If r[i] depends on a, b, c`, then a solution can only be obtained numerically. – Alex Trounev Sep 28 at 18:41