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If (a-b=6) and (ab=16), what is (a^2+b^2)?
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Answer and explanation
Correct answer: 68
Using the identity \((a-b)^2=a^2-2ab+b^2\), we get \(a^2+b^2=(a-b)^2+2ab=6^2+2\times16=36+32=68\). Option 36 is only \((a-b)^2\); the term \(2ab\) must also be added. Exam tip: for \(a^2+b^2\), add \(2ab\) to \((a-b)^2\).
Frequently asked questions
What is the correct answer to this question?
68
Why is this the correct answer?
Using the identity \((a-b)^2=a^2-2ab+b^2\), we get \(a^2+b^2=(a-b)^2+2ab=6^2+2\times16=36+32=68\). Option 36 is only \((a-b)^2\); the term \(2ab\) must also be added. Exam tip: for \(a^2+b^2\), add \(2ab\) to \((a-b)^2\).
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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