zeros of a multivariable function

Hi

I am beginner in matlab, and I need two find two zeros of the following function.

I do not know how I can write its command, the function is:

syms x1 x2 x3 l a b g
% x1:= x, x2: = y, x3: = z, l: = lambda, a:= alpha, b:= beta, g:= damma
f(x1,x2,x3,l,a,b,g)=[-a*x1 - (x2)^2 - (x3)^2 + a*l, 
                     -(x2) +(x1)*(x2) - b*(x1)*(x3) + g, 
                     x3 + b*x1*x2 + x1*x3]
a = 0.25
b = 4
g = 0.5

Answer 1

[Walter Roberson]

syms x1 x2 x3 l 
a = 0.25
b = 4
g = 0.5
f = [-a*x1 - (x2)^2 - (x3)^2 + a*l, 
     -(x2) + (x1)*(x2) - b*(x1)*(x3) + g, 
      x3 + b*x1*x2 + x1*x3];
sol = solve(f, [x1, x2, x3]);
some_random_value_for_l = 1;
X1 = subs(sol.x1, l, some_random_value_for_l);
X2 = subs(sol.x2, l, some_random_value_for_l);
X3 = subs(sol.x3, l, some_random_value_for_l);

vpa([X1, X2, X3])

Now take any two of the five results. For more results, use a different value for some_random_value_for_l

Answer 2

[Star Strider]

Try this (requires the Optimization Toolbox):

syms x1 x2 x3 l a b g
a = 0.25;
b = 4;
g = 0.5;
% x1:= x, x2: = y, x3: = z, l: = lambda, a:= alpha, b:= beta, g:= damma
f(x1,x2,x3)=[(-a*x1 - (x2)^2 - (x3)^2 + a*l),   (-(x2) +(x1)*(x2) - b*(x1)*(x3) + g), (x3 + b*x1*x2 + x1*x3)];
ff = matlabFunction(f, 'Vars',{[x1,x2,x3],l});
l = 1;                                              % Supply The Correct Value For ‘l’
s = fsolve(@(in1) ff(in1,l), rand(1,3));