Symbolic Computations for three non-linear equations solution

Dear community members,

I am trying to find three unknown values A,fu and alpha using three equations:

fl = [1.883806, 1.883135, 1.882170]*10^9;

Qe = [161.43, 10.765, 2.5734]*10^4;

syms A fu alpha

eq1=fl(1)-(1+(A/(Qe(1)^alpha)))*fu==0;

eq2=fl(2)-(1+(A/(Qe(2)^alpha)))*fu==0;

eq3=fl(3)-(1+(A/(Qe(3)^alpha)))*fu==0;

roots = vpasolve(eq1,eq2,eq3,A,fu, alpha)

A = double(roots.A)

alpha = double(roots.alpha)

fu = double(roots.fu)

The results I get:

A: 23.111701126115183488493226207409

fu: 1883037000.0

alpha: 9.7722388976929995256469179038887

Are different from the expected ones:

A = -0.1555;

fu=1.88406316*10^9;

alpha = 0.4967;

Could you please let me know how can I adjust the results?

Answer 1

[Torsten]

fl = [1.883806, 1.883135, 1.882170]*10^9;
Qe = [161.43, 10.765, 2.5734]*10^4;
syms  A fu alpha
eq1=fl(1)-(1+(A/(Qe(1)^alpha)))*fu==0;
eq2=fl(2)-(1+(A/(Qe(2)^alpha)))*fu==0;
eq3=fl(3)-(1+(A/(Qe(3)^alpha)))*fu==0;
roots = vpasolve([eq1,eq2,eq3],[A,fu, alpha],[-0.1555;1.88406316*10^9;0.4967] )

roots = struct with fields:
        A: -0.1770775480947061932261999744466
       fu: 1884030476.7824237850125485618186
    alpha: 0.51096779065904968571811061519679

Anum = double(roots.A)

Anum = -0.1771

alphanum = double(roots.alpha)

alphanum = 0.5110

funum = double(roots.fu)

funum = 1.8840e+09

double(subs([lhs(eq1),lhs(eq2),lhs(eq3)],[A,fu,alpha],[Anum,funum,alphanum]))

ans = 1×3

1.0e-07 * 0.5017 0.4977 0.4929

double(subs([lhs(eq1),lhs(eq2),lhs(eq3)],[A,fu,alpha],[-0.1555,1.88406316*10^9,0.4967]))

ans = 1×3

1.0e+04 * -1.5436 -0.0424 -0.4617

[rfcalculus]

Thank you!