If (m+n=14) and (m^2+n^2=100), what is (mn)?
Answer and explanation
Correct answer: 48
Use the identity \((m+n)^2=m^2+n^2+2mn\). Substituting the given values gives \(14^2=100+2mn\), so \(196=100+2mn\). Hence, \(2mn=96\) and \(mn=48\). Option 96 is a close distractor because it is the value of \(2mn\), not \(mn\). Exam tip: after finding \(2mn\) from this identity, divide by 2 to obtain \(mn\).
Frequently asked questions
What is the correct answer to this question?
48
Why is this the correct answer?
Use the identity \((m+n)^2=m^2+n^2+2mn\). Substituting the given values gives \(14^2=100+2mn\), so \(196=100+2mn\). Hence, \(2mn=96\) and \(mn=48\). Option 96 is a close distractor because it is the value of \(2mn\), not \(mn\). Exam tip: after finding \(2mn\) from this identity, divide by 2 to obtain \(mn\).
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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