Solve for `x` (where `[*]` denotes greatest integer function and `{*}` represent fractional part function)
`(i) [2x]=1` `(ii) {x}^(2)+[x]=2` `(iii) 6{x}^(2)-5{x}+1=0` `(iv) 6{x}^(2)-5{x}-1=0`

Answer

`(i) x in[(1)/(2),1)` `(ii) 2` `(iii) x in uuu_(n in I){n+(1)/(3),n+(1)/(2)}` `(iv) x in [1,2)`