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I am having trouble solving a set of equations using Mathematica 8. I do not get any errors, but I don't get any solutions either.

My parameters and variables are real and non-negative. g is a known, positive constant which I define earlier in my notebook. Also, I have some restrictions on my parameters and variables in the equations. I've tried to implement these using $Assumptions and Assuming[], but it seems like Mathematica ignores this.

Here is my code:

  u == 1/3 μb - 2/3*e, d == 1/3 μb + 1/3*e, 
  2*(u^2 - (g x/2)^2)^(3/2) - (d^2 - (g x/2)^2)^(3/2) -
     (d^2 - (g y/Sqrt[2])^2)^(3/2) - (e^2)^(3/2) == 0, 
  x >= 0,
  y >= 0,
  μb > e,
  μb >= 0,
  u >= 0,
  d >= 0,
  e >= 0}, {u, d, e}, Reals]

μb is a parameter and x and y are variables in some other functions. So what I want is for u, d and e to be functions of x and y, and dependent of μb.

Is there an easy way to solve this in Mathematica 8?

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In what way this this fail? Did you get errors? Did it run for a long time without a result? – Mr.Wizard May 11 '13 at 9:14
It runs a long time without a result. I do not get any errors though. – user7328 May 12 '13 at 8:51
Unless you have numerical values of x and y it looks like a pure algebraic solution of this is unlikely. – Jonathan Shock May 13 '13 at 4:29
Ok. Thanks for the answer. So i probably need to assign values for x and y in a loop and solve theese equations many times and eventually make an InterpolatingFunction for u and d? I know what values x and y should take for different [Mu]b, so i guess this is an alternative at least. Or do you see a faster or easier way out? – user7328 May 14 '13 at 9:22

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