# How to solve a system of equations?

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Denis Stanescu on 27 Feb 2018
Commented: Walter Roberson on 1 Mar 2018
I try to solve a non=linear equtions system, but it doesn't work. I missed something?
F=@(x)[sqrt((x(1)-5)^2 + x(2)^2 + x(3)^2 )-sqrt( x(1)^2 + (x(2)+10)^2 + x(3)^2) +0.34;
sqrt(x(1)^2 + (x(2)+10)^2 + x(3)^2 )-sqrt( x(1)^2 + (x(2)-10)^2 + x(3)^2);
sqrt( x(1)^2 + (x(2)-10)^2 + x(3)^2 )-sqrt( x(1)^2 + x(2)^2 + x(3)^2)];
x0=[50;0;0];
fsolve(F,x0)

Alan Weiss on 27 Feb 2018
You have an errant space just before "+0.34" that is confusing the parser. Try this:
F=@(x)[sqrt((x(1)-5)^2 + x(2)^2 + x(3)^2 )-sqrt( x(1)^2 + (x(2)+10)^2 + x(3)^2)+0.34;
sqrt(x(1)^2 + (x(2)+10)^2 + x(3)^2 )-sqrt( x(1)^2 + (x(2)-10)^2 + x(3)^2);
sqrt( x(1)^2 + (x(2)-10)^2 + x(3)^2 )-sqrt( x(1)^2 + x(2)^2 + x(3)^2)];
x0=[50;0;0];
fsolve(F,x0)
You might need to include some options or a better start point for a good answer.
Alan Weiss
MATLAB mathematical toolbox documentation
##### 2 CommentsShowHide 1 older comment
Walter Roberson on 1 Mar 2018
They are the value of the vector x at the time that fsolve figured out that the system could not be solved.

Roger Stafford on 28 Feb 2018
To solve these you would have to satisfy both
x(1)^2 + (x(2)+10)^2 + x(3)^2 = x(1)^2 + (x(2)-10)^2 + x(3)^2
x(1)^2 + (x(2)-10)^2 + x(3)^2 = x(1)^2 + x(2)^2 + x(3)^2)
and since the x(1) and x(3) terms cancel would require simply
(x(2)+10)^2 = (x(2)-10)^2
(x(2)-10)^2 = x(2)^2
The first of these requires that x(2) = 0 while the second requires that x(2) = 5. These are mutually incompatible and therefore there are no simultaneous solutions to your equations. That is why "it doesn't work".
Denis Stanescu on 28 Feb 2018
when i do that, the solver tell me that there is no solution found, but what are the value from ans?Originally, there should have been the solutions, but if the system doesn't have solutions, what are they? 