Question

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

Answer 1

Answer:

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

Step-by-step 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.