solving a nonlinear set of equations while have a dependency in it

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Sayed
Sayed il 19 Ott 2014
Modificato: Sayed il 21 Ott 2014
I have the following set of 7 equations. There is a dependency between first 6 equations as following:
(Z3^2/Z1)-Z2=(X1^2/X3)-X2
and so I think T have, in fact, 5 equations and that's why I added the last equation as well (to have 6 unknowns and 6 independent eqs.) I solved this system with Mathematica and I know that it should return 2 answers as following:
{a1 -> 2.99957, a2 -> 1.99, a3 -> 0.999892, b1 -> 0.178447, b2 -> -0.19892, b3 -> 0.124498},
{a1 -> 2.99957, a2 -> 2.00, a3 -> 0.999892, b1 -> 0.199952, b2 -> 0.198922, b3 -> 0.199778}
However, in Matlab I couldn't get a solution using "solve". I used the following code; would you please have a look on it and let me know what is the problem (Should I define for "solve" that there is a dependency between first 6 eqs., etc)
Since based on constraint I have in my problem, the solution method must be numerical (and I should be able to adjust the error band) so, "fsolve" is also good here if can return both of the answers for me. (Thanks a lot)
syms a1 a2 a3 b1 b2 b3
X1=0.1866667;
X2=1.9866667;
X3=0.9866667;
Z1=2.96;
Z2=1.96;
Z3=0.16;
E=[a1 b3 b2; % all are my 6 unknowns %
b3 a2 b1;
b2 b1 a3];
L=eig(E);
s=eval(4/3*pi/sqrt(L(1)*L(2)*L(3))); % a volume equation based on unknowns %
[a1, a2, a3, b1, b2, b3]=solve(b1-b2*b3/a1==X1,...
a2-b3^2/a1==X2,...
a3-b2^2/a1==X3,...
a1-b2^2/a3==Z1,...
a2-b1^2/a3==Z2,...
b3-b1*b2/a3==Z3,...
s==1.743);
a1=eval(a1)
a2=eval(a2)
a3=eval(a3)
b1=eval(b1)
b2=eval(b2)
b3=eval(b3)

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