Question

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

Answer 1

The elements of given set are -1, 0 and 1.

Explanation:

The given set is

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

We need to find all the elements of given set.

The given equation is

`x^3-x=0` .... (1)

Solve this equation o find the value of x.

Taking out common factors.

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

Using zero product property,

`x=0`

`x^2-1=0`

`x^2=1`

`x=\pm 1`

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.