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Math Help - How should I solve this question?

  1. #1
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    How should I solve this question?

    Write the reciprocal of 2 + 5sqrt(3) in the form of a + bsqrt(3).

    Thanks !
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  2. #2
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    Quote Originally Posted by beta12 View Post
    Write the reciprocal of 2 + 5sqrt(3) in the form of a + bsqrt(3).

    Thanks !
    The reciprocal is,
    1/(2+5sqrt(3))
    Multiply numerator and denominator by 2-5sqrt(3) thus,
    (2-5sqrt(3))/(4-25*3)=(2/71)+(-5/71)sqrt(3)
    So,

    a=2/71
    b=-5/71

    But this not really a number theory question.
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  3. #3
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    Hi perfecthacker,

    Thanks.

    No, this question is from my number theory book. I thought solving it involving number theory technique.
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  4. #4
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    Quote Originally Posted by beta12 View Post
    No, this question is from my number theory book. I thought solving it involving number theory technique.
    Based on your previous question I assume you are learning how to express quadradic numbers in a periodical continued fraction form. In order to do that it help to rationalize the denomiator of these numbers.
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  5. #5
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    Hi Perfecthacker,

    Yes. You are right.

    Thanks.
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