How to solve a equation that appears z2

Hey, I have this equation to find a solution:

I defined this equation:

 eqn = ((Sig) + (E*(Sig^(const_1))/const_2) - aux == 0)

And the solve I am using this function:

resp =  solve(eqn, Sig)

But in Command Windows appears this message: Warning: Solutions are parameterized by the symbols: z2. To include parameters and conditions in the solution, specify the 'ReturnConditions' value as 'true'.\

Well I search about it and I changed my solve:

resp =  solve(eqn, Sig,'ReturnConditions',true)

and the answer is

Why don't I have the exact number that solves this equation? Solving by hand, I found that the variable Sig is equal to 452.

[Aquatris]

What is Sig in the equation? Share your whole code.

[yogan sganzerla]

This is my hole code Sig is a variable that I would like to find a value.

[Walter Roberson]

yogan, it would help if you posted your entire code including the assignments to const_1, const_2, E, and aux. That would make it easier to check our code for typing mistakes. It is easy to make typing mistakes when we type from images of numbers.

Answer 1

[Stephan]

Hi,

to get numeric solution use:

vpasolve(eqn,Sig)

after assigning values to the other variables.

Best regards

Stephan

[yogan sganzerla]

Dear Stephn, I used vpasolve, and the answer was:

- 450.51324043647629828156483381229 + 96.046628107326123257549527859078i

Well, first there is no reason for the negative in the real part. The second point is that the exact answer is 4.52e+02 and not 450.51. The third point is why an answer is a complex number? I would like a real and positive value of Sig.

Cheers

[Stephan]

Hi,

This is a good example why people should share code instead of pictures from their equations and values... i have tested the anwer i gave you, and checked it against the anwer from Walter. What should i say - i have didferent results in the values than both of you ;-)

But using my method i do not get a complex result, but the first result that is given by Walters method for finding all the solutions to your problem:

syms Sig
E = 6250;
const_1 = 59/9;
const_2 = 7496282746403319;
aux = 7180524015140341 / 17179869184;
eqn = ((Sig) + (E*(Sig^(const_1))/const_2) - aux == 0);
% my answer
stephan_sol = vpasolve(eqn,Sig)
resp = solve(eqn,Sig,'ReturnConditions',true);
% Walters answer
walter_sol = vpa(solve(resp.conditions).^9)
% same value for non complex numbers?
test = double(stephan_sol) == double(walter_sol(1))

So i do not really understand what gone wrong when you tried. But please share your values in a form that they can be copied and pasted to help prevend missunderstandings.

Best regards

Stephan

[Walter Roberson]

I went back in my history, and I see now that I missed a '5' in the numerator for aux, so the 352 I came up with was wrong.

Answer 2

[Walter Roberson]

What the solution is telling you is that eqn has multiple solutions, the 9th power of the set of all values z2 such that z2 satisfies what is in resp.conditions, which holds

z2^59 + (7496282746403319*z2^9)/6250 - 5382511036199773734618773191779/107374182400000 == 0 & -pi/9 < angle(z2) & angle(z2) <= pi/9

You can find the set of values, z2, by doing

sols = solve(resp.conditions)

which gives

 ans =
  root(z^59 + (7496282746403319*z^9)/6250 - 5382511036199773734618773191779/107374182400000, z, 1)
 root(z^59 + (7496282746403319*z^9)/6250 - 5382511036199773734618773191779/107374182400000, z, 18)
 root(z^59 + (7496282746403319*z^9)/6250 - 5382511036199773734618773191779/107374182400000, z, 19)
 root(z^59 + (7496282746403319*z^9)/6250 - 5382511036199773734618773191779/107374182400000, z, 36)
 root(z^59 + (7496282746403319*z^9)/6250 - 5382511036199773734618773191779/107374182400000, z, 37)
 root(z^59 + (7496282746403319*z^9)/6250 - 5382511036199773734618773191779/107374182400000, z, 54)
 root(z^59 + (7496282746403319*z^9)/6250 - 5382511036199773734618773191779/107374182400000, z, 55)

That is telling you that there are 7 solutions, each of which is one specific root of a degree 59 polynomial. And you will have to raise the solutions to the 9th power to get the values for Sig:

>> vpa(solve(resp.conditions).^9)
ans =
                                        352.29770133833260627658225878862
   202.91300541799526990732060006287 - 288.23117984225839253005502676133i
   202.91300541799526990732060006287 + 288.23117984225839253005502676133i
  - 119.3187617653193655735413104768 - 332.12514661176155734260244429285i
  - 119.3187617653193655735413104768 + 332.12514661176155734260244429285i
 - 340.71523389147595562891628070432 - 93.040015788380995959327750986162i
 - 340.71523389147595562891628070432 + 93.040015788380995959327750986162i

[Walter Roberson]

Corrected code:

syms Sig
E = sym(6250);
const_1 = sym(59)/sym(9);
const_2 = sym('7496282746403319');
aux = sym('7180524015140341') / sym('17179869184');
eqn = ((Sig) + (E*(Sig^(const_1))/const_2) - aux == 0)
resp = solve(eqn, 'returnconditions', true);
sols = solve(resp.conditions).^9;
vpa(sols)

ans =
                                        501.11351786727628482805542566572
    288.11758708793446267122185621152 - 410.0513776055818614958938590984i
    288.11758708793446267122185621152 + 410.0513776055818614958938590984i
 - 169.95773946380078795972790346387 - 471.54242429792278622685006803953i
 - 169.95773946380078795972790346387 + 471.54242429792278622685006803953i
 - 483.62567000716230957508622467542 - 131.91490381694147143358175047123i
 - 483.62567000716230957508622467542 + 131.91490381694147143358175047123i