Let R=  the set of real numbers, Z= the set of integers, N= the set of natural numbers. If S be the solution set of the equation (x)2+[x]2=(x−1)2+[x−1]2,  where (x)=  the least integer greater than or equal to x  and [x]= the greatest integer less than or equal tox, then

Given that R=  the set of real numbers, Z= the set of integers, N= the set of natural numbers. The given set of the equation (x)2+[x]2=(x−1)2+[x−1]2 Here (x)=  least integer ≤x For example, (2, 3)=[2, 3]=2 ∴  (x)−[x]=1,   if x is not  integer and [x]=(x) ∴  (x)2+[x]2=(x−1)2+[x+1]2 ⇒(x)2+[x]2=(x)2−2(x)+1+[x]2+2[x]+1 ⇒   −1+1=0   if x∉Z and 0+1≠0    if x∈Z ∴    The solution set S=R−Z .