What is the correct conclusion about A = {x ∈ ℝ : x² + 2 = 2}?
Answer and explanation
Correct answer: A = {0} and A is finite
Starting with x² + 2 = 2, subtract 2 from both sides to obtain x² = 0. The only real number whose square is zero is x = 0. Therefore, the solution set is A = {0}. This is a singleton set containing exactly one element, so it is finite. It is not empty, because zero satisfies the original equation exactly.
Frequently asked questions
What is the correct answer to this question?
A = {0} and A is finite
Why is this the correct answer?
Starting with x² + 2 = 2, subtract 2 from both sides to obtain x² = 0. The only real number whose square is zero is x = 0. Therefore, the solution set is A = {0}. This is a singleton set containing exactly one element, so it is finite. It is not empty, because zero satisfies the original equation exactly.
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.
