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

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

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