Answer:
{-1,0,1}
Step-by-step explanation:
We are given that a set
Suppose A={[tex]x\in R:x^3-x=0[/tex]}
We have to find the all elements of given set
First we solve the given equation
[tex]x^3-x=0[/tex]
[tex]x(x^2-1)=0[/tex]
[tex]x(x+1)(x-1)=0[/tex]
Using the identity:[tex]x^2-y^2=(x+y)(x-y)[/tex]
Substitute each factor equal to zero to find the value of x
[tex]x=0,x-1=0\implies x=1,x+1=0\implies x=-1[/tex]
Hence, the elements in the given set={-1,0,1}
