How many elements are in A = {x : x ∈ Z, x² = 25}?
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Answer and explanation
Correct answer: 2
Solving x² = 25 over the integers gives two solutions: x = 5 and x = −5. Both numbers belong to Z, so A = {−5, 5}. These are distinct elements, and no other integer has square 25. Therefore the cardinality of A, written |A|, is 2. The negative solution must not be omitted.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
Solving x² = 25 over the integers gives two solutions: x = 5 and x = −5. Both numbers belong to Z, so A = {−5, 5}. These are distinct elements, and no other integer has square 25. Therefore the cardinality of A, written |A|, is 2. The negative solution must not be omitted.
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.
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