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Simplifying Complex expression

  • To: mathgroup at smc.vnet.net
  • Subject: [mg43004] Simplifying Complex expression
  • From: Helge Andersson <helge at envic.chalmers.se>
  • Date: Fri, 8 Aug 2003 00:26:20 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello
I'm interested in one of the solution to the the following  equation:
y=3 x^2-2 x^3
in the x-intervall 0 to 1 and for y-values between 0 and 1
With Solve I got three solutions where two of them are complex in general. 
However, it is possible to plot each of them Using the Plot-command in the 
desired domain which I interpretate as they are real-valued with my 
specific conditions. My problem is to simplify the general complex solution 
to one that is real in the domain 0 to 1. The solution that I specifically 
is interested in is the following given in InputForm:

1/2 - (1 - I*Sqrt[3])/(4*(1 + 2*Sqrt[-1 + y]*Sqrt[y] - 2*y)^(1/3)) -
  ((1 + I*Sqrt[3])*(1 + 2*Sqrt[-1 + y]*Sqrt[y] - 2*y)^(1/3))/4

Could someone give me an idea to perform this (for example with Simplify 
Command)

/Helge
Chalmers University of Technology
Sweden


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