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Math Help - compex numbers

  1. #1
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    compex numbers

    solve

    X to the power 15 + 1/ X to the power 25

    when X + 1/X = 1
    Last edited by sktulika; May 22nd 2008 at 09:43 PM.
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  2. #2
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    Quote Originally Posted by sktulika View Post
    solve
    X 15 +1/X 25

    If X + 1/X =1
    Does X 15 mean 15 X or X^15 .....? Does 1/X 25 mean 1/X^25, 1/(25 X) or 25/X .....?

    Much greater clarity is required.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Does X 15 mean 15 X or X^15 .....? Does 1/X 25 mean 1/X^25, 1/(25 X) or 25/X .....?

    Much greater clarity is required.
    So you want to find the value of x^{15} + \frac{1}{x^{25}} given that x + \frac{1}{x} = 1.

    A brutal approach:

    x + \frac{1}{x} = 1 \Rightarrow x^2 - x + 1 = 0 \Rightarrow x = ....... Express the solution in polar form.


    x^{15} + \frac{1}{x^{25}} = \frac{1}{x^{25}} (x^{40} + 1). Substitute the polar form of x, use de Moivre's theorem and tidy up.
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