Three nonlinear equation with initial guess

How can I solve this question? Please help me, Thank you.

equations are

-0.06*(x^2)-1.06*(z^2)+3.18*x+3.18*z+1.59*y-2.06*x*y-3.12*x*z-2.385-1.06*y*z=0

2.63*(x^2)-1.63*(y^2)-2.63*(z^2)-3.945*x+3.945*y+3.945*z-4.76*y*z=0

z-7.5*y+5x*y+5*y*z=0

initial guess x=y=z=0

x=?

y=?

z=?

[MOSLI KARIM]

function bvp_prb14



tspan=[0; 15];
y0=[0;0;0];


[t,x]=ode45(@fct,tspan,y0)

X=x(:,1)  %%%  x solution 
Y=x(:,2)  %%% YOUR Y
Z=x(:,3) %%%YOUR Z 
table(X,Y,Z)
function yp=fct(t,x)

yp=[-0.06*(x(1)^2)-1.06*(x(3)^2)+3.18*x(1)+3.18*x(3)+1.59*x(2)-2.06*x(1)*x(2)-3.12*x(1)*x(3)-2.385-1.06*x(2)*x(3);
2.63*(x(1)^2)-1.63*(x(2)^2)-2.63*(x(3)^2)-3.945*x(1)+3.945*x(2)+3.945*x(3)-4.76*x(2)*x(3);
x(3)-7.5*x(2)+5*x(1)*x(2)+5*x(2)*x(3)];
end 

end

Answer 1

[Torsten]

fun = @(x,y,z)[-0.06*(x^2)-1.06*(z^2)+3.18*x+3.18*z+1.59*y-2.06*x*y-3.12*x*z-2.385-1.06*y*z;2.63*(x^2)-1.63*(y^2)-2.63*(z^2)-3.945*x+3.945*y+3.945*z-4.76*y*z;z-7.5*y+5*x*y+5*y*z];
u0=[0; 0; 0];
[sol,fval]=fsolve(@(u)fun(u(1),u(2),u(3)),u0)

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.

sol = 3×1

0.7079 0.1909 0.3868

fval = 3×1

1.0e-10 * -0.0873 0.4509 0.4931

Answer 2

[Bjorn Gustavsson]

Have a look at the help and documentation of fsolve. That should be the function for this task

HTH

Answer 3

[Walter Roberson]

with the symbolic toolbox you can find 8 solutions including a complex conjugate pair. The real solutions are approximately

    0.7079    0.1909    0.3868
    0.0375    0.5366    1.0654
    0.9235   -0.3927    1.1749
    0.6229   -0.5919    1.3247
   -0.4412   -3.4575    2.0604
    0.0323   -0.6798    2.0795

As you start from 0,0,0 the implication is that negative components are valid