Which set is A = {x ∈ ℝ : x² + 1 = 2x} equal to?
Answer and explanation
Correct answer: A = {1}
Rewrite the equation as x² − 2x + 1 = 0. This expression is a perfect square: (x − 1)² = 0. Hence the only real solution is x = 1. Although the root is repeated algebraically, a set does not record multiplicity; it contains the value only once. Therefore the solution set is the singleton set A = {1}, not a two-element set and not the empty set.
Frequently asked questions
What is the correct answer to this question?
A = {1}
Why is this the correct answer?
Rewrite the equation as x² − 2x + 1 = 0. This expression is a perfect square: (x − 1)² = 0. Hence the only real solution is x = 1. Although the root is repeated algebraically, a set does not record multiplicity; it contains the value only once. Therefore the solution set is the singleton set A = {1}, not a two-element set and not the empty set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
