MATLAB: Cannot solve symbolically returning a numeric approximation

MATLABSymbolic Math Toolboxwarning: cannot solve symbolically.

Hello, I am trying to solve the function shown in the figure below in terms of (k) but I am getting this warnning, the function is attached as an image. now this is how I solved it.
   function [k] = Calculatek()
   P`=0.5, P = 10000, k should be 75
   P  =  input('Please Enter value of P : ');
   Pd =  input('Please Enter value of P''' );
   K=sym( 'K')  % define symbolic function for equation solver
   num= (1-K/P)^(2*(P-K+0.5));
   den= (1-2*K/P)^(P-2*K+0.5);
   fun=Pd-( 1 - (num/den));
   Temp=solve(fun);
   k= double(Temp);
now I know for a fact that if P = 100000 and p' = 0.5, k should be 250 and if P = 10000 and p' = 0.5 k should be 75.
I am sure Matlab can solve this but I keep on getting this :
   >> Calculatek
   Please Enter value of P : 100000
   Please Enter value of P'0.5
   K =
   K
   Warning: Cannot solve symbolically.
   Returning a numeric approximation instead. 
   > In solve (line 305)
   In Calculatek (line 19) 
   ans =
   -263.6242
which I am sure is not correct
what I am doing wrong? can anyone help.
thanks

Best Answer

P = 10000
Pd = 0.5;
syms K
num= (1-K/P)^(2*(P-K+0.5));
den= (1-2*K/P)^(P-2*K+0.5);
fun=Pd-( 1 - (num/den));
pretty(fun)
                  20001
            2 K - -----
/       K  \        2   /       K   \20001 - 2 K   1
| 1 - ---- |            | 1 - ----- |            - -
\     5000 /            \     10000 /              2
Problems with big exponents are always dangerous to try to solve. However, IF you give the solver a hint of which solution you are interested in...
vpasolve(fun,100)
ans =
82.911209433548073806263919152479
I don't know how you decided that 75 was the solution. That seems to be a bit off, as is verified by the plot. So I might disagree with your claim of FACT.
ezplot(fun,[50,100])
grid on
Related Question