Question

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

Answer 1

Answer:

{-1,0,1}

Step-by-step 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}