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Math Help - Geometric progression

  1. #1
    MHF Contributor alexmahone's Avatar
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    Geometric progression

    Find all real x>o such that x-[x], [x], x (where [x] denotes the greatest integer not greater than x) form a geometric progression.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by alexmahone View Post
    Find all real x>o such that x-[x], [x], x (where [x] denotes the greatest integer not greater than x) form a geometric progression.
    write x=a+b, where a=[x] and 0<=b<1. Then the condition that b,a,a+b are a geometric progressions is:

    a/b=(a+b)/a

    solve this for a in terms of b then conclude what you must from the requirerment that a is an integer, then reconstruct x in terms of b.

    CB
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