For what positive numbers will the cube of a number be less

For what positive numbers will the cube of a number be less than the number?

Solution

let x be the number

x^3 < x

x (x^2 -1) < 0

x( x+1) (x-1) <0

x< -1 , 0<x<1

since we need only positive number

the number should lie between 0 and 1

x^3<x for 0<x<1