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If \(a-b=8\) and \(ab=12\), what is the value of \(a^2+b^2\)?
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Answer and explanation
Correct answer: 88
Use the identity \(a^2+b^2=(a-b)^2+2ab\). Thus, \(a^2+b^2=8^2+2(12)=64+24=88\). The value 76 results from adding only \(ab\) instead of \(2ab\), so it is incorrect. In exams, carefully identify the sign and the coefficient of \(2ab\) in the relevant identity.
Frequently asked questions
What is the correct answer to this question?
88
Why is this the correct answer?
Use the identity \(a^2+b^2=(a-b)^2+2ab\). Thus, \(a^2+b^2=8^2+2(12)=64+24=88\). The value 76 results from adding only \(ab\) instead of \(2ab\), so it is incorrect. In exams, carefully identify the sign and the coefficient of \(2ab\) in the relevant identity.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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