MATLAB: How can i solve this equation 1/(24*(x^4/24 + x^3/24 + x^2/24 + x/24 + 1/24))

Question

Hi everyone,

I am very new to Matlab, ive spent quite a great deal trying to solve this equaition for x.

I've read through alot of the forums and tried solve, fsolve, roots, vpasolve, however i keep ending up with the same answer when running the code : Empty sym: 0-by-1

Here is the code i am executing. I am trying to calculate traffic in Erlangs using the blockage probability and number of ressources availables and the formula

 if erlint == 0 && probint ~=0 && circint ~=0
    P = str2double(prob);
    m = str2double(circ);
    syms x
    assume(x ~= 0)
    assumptions(x)
    somme=0;
 for k=0:m
    kfact= factorial(m);
    somme=somme + (x^k)/(kfact);
 end
    somme
    eqn2 = (x^m/f)/(x^k)/(somme);
      
    eqn2

Here is the output up until the result above.

ans =
x ~= 0
somme =
x^4/24 + x^3/24 + x^2/24 + x/24 + 1/24
eqn2 =
1/(24*(x^4/24 + x^3/24 + x^2/24 + x/24 + 1/24)).

x will represent the value i am trying to calculate based on the 2 other.

Any help will be greatly appreciated.

Thanks!

Answer 1

I don’t believe there is a solution in the sense that:

Eqn1 = 1/(24*(x^4/24 + x^3/24 + x^2/24 + x/24 + 1/24)) == 0;

because this is the essential equivalent of a much simpler equation:

Eqn = 1/(x + 1) == 0;

Consider:

L = limit(Eqn, x, Inf)
L = 0

and the only solution is :

x -> Inf