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Math Help - A simple Binomial expansion question

  1. #1
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    A simple Binomial expansion question

    For the first parts of the question I had to expand (1+8x)^\frac{1}{2} = 1+4x-8x^2 and     (1-4x)^\frac{1}{2} = 1+2x+6x^2

    The next part is to find \sqrt{(1+8x)/(1-4x)}
    I can't get anywhere near the answer in the book, having tried dividing/multiplying the two expansions...
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  2. #2
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    Quote Originally Posted by JeWiSh View Post
    For the first parts of the question I had to expand (1+8x)^\frac{1}{2} = 1+4x-8x^2 and  (1-4x)^\frac{1}{2} = 1+2x+6x^2

    The next part is to find \sqrt{(1+8x)/(1-4x)}
    I can't get anywhere near the answer in the book, having tried dividing/multiplying the two expansions...
    Those expansions are nonsense.
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    Quote Originally Posted by Prove It View Post
    Those expansions are nonsense.
    They are? They're just approximations, up to the x^2 term. The book says they're right...
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    Quote Originally Posted by JeWiSh View Post
    They are? They're just approximations, up to the x^2 term. The book says they're right...
    You should have said that when you used them.
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    Quote Originally Posted by mr fantastic View Post
    You should have said that when you used them.
    Sorry...can anyone get me started?
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    Quote Originally Posted by JeWiSh View Post
    For the first parts of the question I had to expand (1+8x)^\frac{1}{2} = 1+4x-8x^2 and  (1-4x)^\frac{1}{2} = 1+2x+6x^2

    The next part is to find \sqrt{(1+8x)/(1-4x)}
    I can't get anywhere near the answer in the book, having tried dividing/multiplying the two expansions...
    You mean find an approximate expression for \sqrt{(1+8x)/(1-4x)}, right .... ? To what degree?
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  7. #7
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    Quote Originally Posted by mr fantastic View Post
    You mean find an approximate expression for \sqrt{(1+8x)/(1-4x)}, right .... ? To what degree?
    To the  x^2 term I think, since that's what I was supposed to expand the original expressions to.
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