AuEN Ratio

Algebra Level 4

Let xR+x \in R^{+} such that {x},[x],x\{x\} , [x] , x are in a geometric progression. What is the common ratio of the G.P. ?

Notations: [x][x] denotes the greatest integer less than xx while {x}\{x\} is defined to be x[x]x-[x]. You may refer to the Wikipedia link for more information about these notations.

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