The solution of x−1=(x−[x])(x−{x})  (where [x]  and {x}  are the integral and fractional part of x ) is :

∵            (x−1)=(x−[x])(x−{x}) ⇒            x=1+{x}[x] ⇒          [x]+{x}=1+{x}[x] ⇒          ({x}−1)([x]−1)=0          {x}−1≠0,      ∴    [x]−1=0                [x]=1    ⇒x∈[1,2)