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(I want to solve this equation for r. while using solve command I am getting roots not in explicit form, but using #1 square cube etc.)

x = 4 + (3 E1^2 - 4) r + (1 - E1^2) r^2 + 
  2 b (2 - r) Sqrt[(-2 + r) r^2 (2 + (-1 + E1^2) r)]

{{r -> Root[-16 + (32 - 24 E1^2) #1 + (-24 - 64 b^2 + 32 E1^2 - 
         9 E1^4) #1^2 + (8 + 128 b^2 - 14 E1^2 - 32 b^2 E1^2 + 
         6 E1^4) #1^3 + (-1 - 96 b^2 + 2 E1^2 + 48 b^2 E1^2 - 
         E1^4) #1^4 + (32 b^2 - 24 b^2 E1^2) #1^5 + (-4 b^2 + 
         4 b^2 E1^2) #1^6 &, 1]}, {r -> 
   Root[-16 + (32 - 24 E1^2) #1 + (-24 - 64 b^2 + 32 E1^2 - 
         9 E1^4) #1^2 + (8 + 128 b^2 - 14 E1^2 - 32 b^2 E1^2 + 
         6 E1^4) #1^3 + (-1 - 96 b^2 + 2 E1^2 + 48 b^2 E1^2 - 
         E1^4) #1^4 + (32 b^2 - 24 b^2 E1^2) #1^5 + (-4 b^2 + 
         4 b^2 E1^2) #1^6 &, 2]}, {r -> 
   Root[-16 + (32 - 24 E1^2) #1 + (-24 - 64 b^2 + 32 E1^2 - 
         9 E1^4) #1^2 + (8 + 128 b^2 - 14 E1^2 - 32 b^2 E1^2 + 
         6 E1^4) #1^3 + (-1 - 96 b^2 + 2 E1^2 + 48 b^2 E1^2 - 
         E1^4) #1^4 + (32 b^2 - 24 b^2 E1^2) #1^5 + (-4 b^2 + 
         4 b^2 E1^2) #1^6 &, 3]}, {r -> 
   Root[-16 + (32 - 24 E1^2) #1 + (-24 - 64 b^2 + 32 E1^2 - 
         9 E1^4) #1^2 + (8 + 128 b^2 - 14 E1^2 - 32 b^2 E1^2 + 
         6 E1^4) #1^3 + (-1 - 96 b^2 + 2 E1^2 + 48 b^2 E1^2 - 
         E1^4) #1^4 + (32 b^2 - 24 b^2 E1^2) #1^5 + (-4 b^2 + 
         4 b^2 E1^2) #1^6 &, 4]}, {r -> 
   Root[-16 + (32 - 24 E1^2) #1 + (-24 - 64 b^2 + 32 E1^2 - 
         9 E1^4) #1^2 + (8 + 128 b^2 - 14 E1^2 - 32 b^2 E1^2 + 
         6 E1^4) #1^3 + (-1 - 96 b^2 + 2 E1^2 + 48 b^2 E1^2 - 
         E1^4) #1^4 + (32 b^2 - 24 b^2 E1^2) #1^5 + (-4 b^2 + 
         4 b^2 E1^2) #1^6 &, 5]}, {r -> 
   Root[-16 + (32 - 24 E1^2) #1 + (-24 - 64 b^2 + 32 E1^2 - 
         9 E1^4) #1^2 + (8 + 128 b^2 - 14 E1^2 - 32 b^2 E1^2 + 
         6 E1^4) #1^3 + (-1 - 96 b^2 + 2 E1^2 + 48 b^2 E1^2 - 
         E1^4) #1^4 + (32 b^2 - 24 b^2 E1^2) #1^5 + (-4 b^2 + 
         4 b^2 E1^2) #1^6 &, 6]}}```

(how can I get the specific form in Mathematica?)

Vaseem Akram
  • 1
  • What's known about r,b,E1? Are you looking for real solutions? – Ulrich Neumann Aug 15 '22 at 08:02
  • Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Take the tour! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! – Michael E2 Aug 15 '22 at 12:08
  • What specific form do you seek? See https://mathematica.stackexchange.com/questions/13767/how-do-i-work-with-root-objects for more on the form of the answer shown in the question. – Michael E2 Aug 15 '22 at 20:08

0 Answers0