Question

Find total number of solutions of [x]^2= x + 2 {x}, where (.) and {.} denotes the greatest integer

function and fractional part.

Answer 1

Explanation:

There are only 5 solutions:

x=-1

x=-1/3

x=0

x=1

x=8/3

See the graph

In blue: y=[x]²

In red : y=x+2(x-[x])