If (m+n=12) and (m-n=4), what is the value of (mn)?
Answer and explanation
Correct answer: 32
Use the identity \((m+n)^2-(m-n)^2=4mn\). Substituting the given values gives \(12^2-4^2=4mn\), i.e., \(144-16=4mn\). Hence \(128=4mn\), so \(mn=32\). Option 16 may result from an incorrect division of 128 by 4. Exam tip: In such questions, square the two given expressions first and then take their difference.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
Use the identity \((m+n)^2-(m-n)^2=4mn\). Substituting the given values gives \(12^2-4^2=4mn\), i.e., \(144-16=4mn\). Hence \(128=4mn\), so \(mn=32\). Option 16 may result from an incorrect division of 128 by 4. Exam tip: In such questions, square the two given expressions first and then take their difference.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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