Question

Write down all elements of the set {XER: X3 -x = 0).

Answer 1

{-1,0,1}

Explanation:

We are given that a set

Suppose A={
`x\in R:x^3-x=0`}

We have to find the all elements of given set

First we solve the given equation

`x^3-x=0`

`x(x^2-1)=0`

`x(x+1)(x-1)=0`

Using the identity:
`x^2-y^2=(x+y)(x-y)`

Substitute each factor equal to zero to find the value of x

`x=0,x-1=0\implies x=1,x+1=0\implies x=-1`

Hence, the elements in the given set={-1,0,1}