Answer:
The elements of given set are -1, 0 and 1.
Step-by-step explanation:
The given set is
[tex]\{x\in R:x^3-x=0\}[/tex]
We need to find all the elements of given set.
The given equation is
[tex]x^3-x=0[/tex] .... (1)
Solve this equation o find the value of x.
Taking out common factors.
[tex]x(x^2-1)=0[/tex]
Using zero product property,
[tex]x=0[/tex]
[tex]x^2-1=0[/tex]
[tex]x^2=1[/tex]
[tex]x=\pm 1[/tex]
All rational and irrational numbers are real numbers.
On solving equation (1) we get x = -1, 0, 1. All these numbers are real number. So, the elements of given set are -1, 0 and 1. The set is defined as
{ -1, 0, 1}
Therefore, the elements of given set are -1, 0 and 1.
