Take the 2-minute tour ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

I want to solve following equation:

Solve[{g^2 - gamma*alpha + alpha^2 - 
    omega*(omega*alpha)/(gamma - 2*alpha) - (omega^2*
       alpha^2)/(gamma - 2*alpha)^2 == 0, gamma > 0, omega > 0, 
  g > 0}, alpha]

I want to become an analytic, explicit expression for alpha, but Mathematica gives me only a solution with Root; for example, (there are more solutions):

{alpha -> 
  ConditionalExpression[
   I Root[g^2 gamma^2 - 
        4 g^2 gamma Root[
          g^2 gamma^2 + (-4 g^2 gamma - gamma^3 - 
               gamma omega^2) #1 + (4 g^2 + 5 gamma^2 + 
               omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1] - 
        gamma^3 Root[
          g^2 gamma^2 + (-4 g^2 gamma - gamma^3 - 
               gamma omega^2) #1 + (4 g^2 + 5 gamma^2 + 
               omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1] - 
        gamma omega^2 Root[
          g^2 gamma^2 + (-4 g^2 gamma - gamma^3 - 
               gamma omega^2) #1 + (4 g^2 + 5 gamma^2 + 
               omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1] + 
        4 g^2 Root[
          g^2 gamma^2 + (-4 g^2 gamma - gamma^3 - 
               gamma omega^2) #1 + (4 g^2 + 5 gamma^2 + 
               omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1]^2 + 
        5 gamma^2 Root[
          g^2 gamma^2 + (-4 g^2 gamma - gamma^3 - 
               gamma omega^2) #1 + (4 g^2 + 5 gamma^2 + 
               omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1]^2 + 
        omega^2 Root[
          g^2 gamma^2 + (-4 g^2 gamma - gamma^3 - 
               gamma omega^2) #1 + (4 g^2 + 5 gamma^2 + 
               omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1]^2 - 
        8 gamma Root[
          g^2 gamma^2 + (-4 g^2 gamma - gamma^3 - 
               gamma omega^2) #1 + (4 g^2 + 5 gamma^2 + 
               omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1]^3 + 
        4 Root[g^2 gamma^2 + (-4 g^2 gamma - gamma^3 - 
               gamma omega^2) #1 + (4 g^2 + 5 gamma^2 + 
               omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 
          1]^4 + (-4 g^2 - 5 gamma^2 - omega^2 + 
           24 gamma Root[
             g^2 gamma^2 + (-4 g^2 gamma - gamma^3 - 
                  gamma omega^2) #1 + (4 g^2 + 5 gamma^2 + 
                  omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1] - 
           24 Root[
             g^2 gamma^2 + (-4 g^2 gamma - gamma^3 - 
                  gamma omega^2) #1 + (4 g^2 + 5 gamma^2 + 
                  omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 
             1]^2) #1^2 + 4 #1^4 &, 2] + 
    Root[g^2 gamma^2 + (-4 g^2 gamma - gamma^3 - 
          gamma omega^2) #1 + (4 g^2 + 5 gamma^2 + omega^2) #1^2 - 
       8 gamma #1^3 + 4 #1^4 &, 1], g > 0 && gamma > 0 && omega > 0]}

This is not an explicit solution. I have also tried Reduce without success.

What can I do?

share|improve this question
    
As a response indicates, you can just convert the Root functions into radicals. But actually the Root things themselves are explicit, and for many purposes they are better behaved than parametrized radicals. –  Daniel Lichtblau Feb 26 '13 at 14:23
add comment

1 Answer 1

up vote 3 down vote accepted
Solve[{g^2 - gamma alpha + alpha^2 - (omega (omega alpha))/(
      gamma - 2 alpha) - (omega^2 alpha^2)/(gamma - 2 alpha)^2 == 0, 
    gamma > 0, omega > 0, g > 0}, alpha, Reals] // ToRadicals // Simplify
share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.