If U = {x ∈ ℤ : x³ = x}, which is the roster form of U?
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Answer and explanation
Correct answer: U = {−1, 0, 1}
Rewrite the equation as x³ − x = 0 and factor it: x(x² − 1) = 0, so x(x − 1)(x + 1) = 0. The possible solutions are x = 0, x = 1, and x = −1. All three are integers and therefore satisfy the restriction x ∈ ℤ. Hence the set is U = {−1, 0, 1}, making option A correct.
Frequently asked questions
What is the correct answer to this question?
U = {−1, 0, 1}
Why is this the correct answer?
Rewrite the equation as x³ − x = 0 and factor it: x(x² − 1) = 0, so x(x − 1)(x + 1) = 0. The possible solutions are x = 0, x = 1, and x = −1. All three are integers and therefore satisfy the restriction x ∈ ℤ. Hence the set is U = {−1, 0, 1}, making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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