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Combinatorics and roots

  1. May 10, 2007 #1
    1. The problem statement, all variables and given/known data

    The following is a question from a set-text that I have chosen to explore.

    What digit is imediately to the right of the decimal point in (sqrt(3) + sqrt(2))^2002

    2. Relevant equations



    3. The attempt at a solution

    I have not gone very far with this, and may need to find a different problem. What I have done is explore (sqrt(3) + sqrt(2))^n, for n = 0, 1, 2, 3, 4... and found that for even values of n (which include 2002) that the expression evaluates to the sum of a constant and a constant multiple of sqrt(6). Both constants are too large to calculate.

    I also know that [(sqrt(3) + sqrt(2))^2002][(sqrt(3) - sqrt(2))^2002]=1, but I am not sure if that can be used to find a solution.

    I am presently exploring [(sqrt(3) + sqrt(2))^2002]-[(sqrt(3) - sqrt(2))^2002] and find that a whole lot of terms are being cancelled.

    Any suggestions would be appreciated,

    Thanks.
    :surprised
     
  2. jcsd
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