Question

The total number of solutions of x square = x +2{x}, where [] and {.} denote the greatest
integer function and fractional part function respectively, is equal to​

Answer 1

Answer:

We can write any real number x as sum of its integral part and fractional part. Thus x=[x]+{x}⟹{x}=x−[x]

.

Therefore given equation becomes x=[x]

.

Thus x

has to be an integer. Hence solution set is x∈Z.