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Talor series expansion of roots of algebraic equation

  1. Dec 3, 2012 #1
    I have a algebraic equation like so:
    x^2-1-εx=0

    the roots are obviously-
    x=ε/2±√(1+ε^2/4)

    How can I expand the expression for the roots- as a taylor series?

    the answer is given as:
    x(1)=1+ε/2+ε^2/8+O(ε^3)

    I am assuming the author expanded the root 'x' in terms of ε before hand and substituted in the algebraic.Is that even allowed?
     
  2. jcsd
  3. Dec 3, 2012 #2

    mathman

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    Science Advisor

    Use the binomial theorem on √(1+ε^2/4) = (1 + ε2/4)1/2 = 1+ε2/8 + O(ε4)
     
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