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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Originally Posted by alexmahone 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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