If R = {x : x ∈ ℤ and x³ = x}, then R is:
Advertisement
Answer and explanation
Correct answer: R = {-1, 0, 1}
We solve the defining equation x³ = x by bringing all terms to one side: x³ − x = 0. Factoring gives x(x² − 1) = 0, or x(x − 1)(x + 1) = 0. Therefore, x can be 0, 1, or −1. All three values are integers, so all satisfy the condition defining R. Hence the set is R = {−1, 0, 1}, which is option A.
Frequently asked questions
What is the correct answer to this question?
R = {-1, 0, 1}
Why is this the correct answer?
We solve the defining equation x³ = x by bringing all terms to one side: x³ − x = 0. Factoring gives x(x² − 1) = 0, or x(x − 1)(x + 1) = 0. Therefore, x can be 0, 1, or −1. All three values are integers, so all satisfy the condition defining R. Hence the set is R = {−1, 0, 1}, which is option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
Advertisement