The solution set for [x] {x} = 1 (where {x} and [x] are, respectively, fractional part function and greatest integer function) is

xx=1Obviously, x cannot be negative.Further, x≠0.For  x=1,x=1,  whichisnotpossible.Hence,  x∉0,2.For   x∈2,3,x=2  or  x=12 or  x=52=2+12For   x∈3,4,x=3  or  x=13  or  x=3+13.For  x∈4,5,x=4  or  x=14  or  x=4+14Thus, solution is x=m+1m,   where  m∈N-1.