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Sum of reciprocals of integers is given - find integers

  1. Apr 1, 2009 #1
    1. The problem statement, all variables and given/known data
    The sum of the reciprocals of two consecutive odd integers is 28/195. Find the two integers.


    2. Relevant equations
    ?


    3. The attempt at a solution
    28/195= 1/x + 1/(x-2)
    Solved using quadratic formula and got 3.44, which does not seem to be right.. Any help?
     
  2. jcsd
  3. Apr 1, 2009 #2

    symbolipoint

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    Re: Algebra

    "Two consecutive odd integers...", you have then two numbers to start with:
    2n+1, and 2n+3. The 'n' is a variable and the factor of 2 ensures that the entire expression will be ODD. Note that 'n' will be an integer.
     
  4. Apr 2, 2009 #3

    HallsofIvy

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    Re: Algebra

    Using "x" and "x-2" is just as valid as "2n+3" and "2n+1" so the equation you have, 1/x+ 1/(x-2)= 28/195 is perfectly good. Unfortunately, you have left out the important part: you don't show how you got 3.44. 1/x+ 1/(x-2)= 28/195, after you multiply the entire equation by 195x(x-2) becomes a quadratic formula and I get two integer solutions.
     
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