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Total number of positive real value of x...

Total number of positive real value of x such that `x,[x],(x)` are H.P, where [.] denotes the greatest integer function and (.) denotes fraction part is equal To :

Text Solution

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x=I+F
I- integer part
F-fractional part.
x,[x],{x} are in HP.
`1/(I+F),1/I,1/F` are in AP
`2/I=1/(I+F)+1/F`
`2/I=(I+2F)/(F(I+F)`
`2F(I+F)=I(I+2F)`
...
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