That square root looks to be malformed. Also I don't see how this type of elimination will be helpful in terms of getting a smaller solution to the biquadratic.

Hi Daniel, Thanks for reply.
1) I attached the code. 2) I used series to do x<<D (much lesser than) approximation. In the code, I wrote both methods to solve the quartic equation. Both give me quartic equation solution in which 3rd and 1st power coefficients are zeros. However the coefficient values and solutions are different. First method using series approximation, gave me very lengthy solution. The second method by hand gave me simpler solution but still it is a long one. My question is: Which method is consistent approximation? Are there commands to do condition (much lesser than)? Any other options of calculating the limits such that x variable is still present in equation? For last method, FullSimplify does the job in simplifying the results.

Attachments:

Thanks Daniel, I will start working on it and see what happens.

Hi Daniel,

I think I might solve it if I get rid of square roots in it. I attempted to expand the f5 function in order to get rid of square roots because for my situation Det[f5]==0. I attempted by using Eliminate command as well as GroebnerBasis command. For some reasons it does not work...it takes more than 15 minutes.

eli=ReplaceAll[Sqrt[f5,D^2 - (x - c)^2]->u]
Eliminate[{eli==0,u^2==D^2 - (x - c)^2},u]
GroebnerBasis[{eli,u^2-D^2 + (x - c)^2},x,u]

Am I right with the code?

Hi Robert, Yes I tried FullSimplify. The system was busy for a long time, that I usually aborted the calculations after 5 minutes. Perhaps next time I should try a bit longer.