I have a parametric nonlinear function which is literally a nightmare. I know roots exist, they are real and the two parameters,
p,e are both positive. What I was expecting from mathematica was to get a solution (in form of a root, no closed form) but even letting the program working all night I surrendered. I can't understand if it's me framing the problem not in an efficient way, it's my pc which needs serious upgrades or the problem that is simply too hard for methods like Reduce or Solve. If the case is the latter, I guess I'm doomed... Any hint towards the other two? Thanks for the help.
My attempts and the equation:
f[x_]:=(1/(8 (p^2+x^2)^3))p^2 (-2 p^6+p^5 (4-8 x)+2 p^3 (3-8 x) x^2-6 p x^4+p^4 (80000+2 x-9 x^2)+2 p^2 x (40000+60000 x+x^2-5 x^3)-3 x^3 (-80000+40000 x+x^3)+(4 Sqrt e x (p^2+x^2)^2 (2 p x^3+p^4 (-2+3 x)+2 p^3 x (-3+4 x)+x^2 (-80000+40000 x+x^3)+2 p^2 (40000-60000 x-x^2+2 x^3)))/Sqrt[-e p^2 (-1+x) x^2 (p^2+x^2)^2 (-40000+p^2+2 p x+x^2)]) Reduce[f[x]==0 && x>=0 &&p>=0 && e>=0,x,Reals] (*stuck running*) Solve[f[x]==0 && x>=0 &&p>=0 && e>=0,x,Reals] (*stuck running*)