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Simplify Completley x^3 - 27

  1. Aug 15, 2010 #1
    1. The problem statement, all variables and given/known data

    I got down to here and didn't know where to go from here
    http://www.wolframalpha.com/input/?...)(1-i^(-4/3))))(x+3/2(1+i^(2/3)(1-i^(-4/3))))
    see the input value on that link if you don't feel like reading the equation below

    (x-3) (x-3/2 (-1+i^(2/3) (1-i^(-4/3)))) (x+3/2 (1+i^(2/3) (1-i^(-4/3))))

    now my question is how come wolfram tells me that the exact result is
    (x-3) (x-3/2 ((-1)^(1/3) (1+(-1)^(1/3))-1)) (x+3/2 (1+(-1)^(1/3) (1+(-1)^(1/3))))
    again click on the link to see the "exact result" if you don't want to read the equation like this

    the two are not equal to each other by any means what's up with this?
    Also the end result that I'm suppose to get to apparently is this

    x^3+3/2 (1+e^((i pi)/3) (1+e^((i pi)/3))) x^2-3/2 (-1+e^((i pi)/3) (1+e^((i pi)/3))) x^2-3 x^2-9/4 (-1+e^((i pi)/3) (1+e^((i pi)/3))) (1+e^((i pi)/3) (1+e^((i pi)/3))) x-9/2 (1+e^((i pi)/3) (1+e^((i pi)/3))) x+9/2 (-1+e^((i pi)/3) (1+e^((i pi)/3))) x+27/4 (-1+e^((i pi)/3) (1+e^((i pi)/3))) (1+e^((i pi)/3) (1+e^((i pi)/3)))

    the last alternate form on wolfram link above and currently i'm at the input form of x^3 - 27

    (x-3) (x-3/2 (-1+i^(2/3) (1-i^(-4/3)))) (x+3/2 (1+i^(2/3) (1-i^(-4/3))))

    any help in getting to that anser would be great as I don't know how to...
     
  2. jcsd
  3. Aug 15, 2010 #2
    The expressions are the same....wolfram replace i's with square roots of -1...but they are equivalent....
    I don't really understand your question, you asked to simplify x^3-27...where do all these equations come from?
     
  4. Aug 16, 2010 #3

    ehild

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    Homework Helper
    Gold Member

    Did you mean "factorize"? x^3-27=x^3-3^3, so you can factor out x-3: x^3-3^3=(x-3)(x^2+3x+9). x^2+3x+9 can be factorized further as (x-u)(x-v) where u and v are the (complex) roots of x^2+3x+9=0.

    ehild
     
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