Q:

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

Accepted Solution

A:
Answer:The elements of given set are -1, 0 and 1.Step-by-step explanation:The given set is[tex]\{x\in R:x^3-x=0\}[/tex]We need to find all the elements of given set.The given equation is[tex]x^3-x=0[/tex]           .... (1)Solve this equation o find the value of x.Taking out common factors.[tex]x(x^2-1)=0[/tex]Using zero product property,[tex]x=0[/tex][tex]x^2-1=0[/tex][tex]x^2=1[/tex][tex]x=\pm 1[/tex]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.