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If \(a-b=5\) and \(ab=6\), what is the value of \(a^2+b^2\)?
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Answer and explanation
Correct answer: 37
Use the identity \(a^2+b^2=(a-b)^2+2ab\). Thus, \(a^2+b^2=5^2+2(6)=25+12=37\). Option B results from incorrectly adding only \(ab\) instead of \(2ab\). In exams, remember that \((a-b)^2=a^2-2ab+b^2\), which leads to this identity.
Frequently asked questions
What is the correct answer to this question?
37
Why is this the correct answer?
Use the identity \(a^2+b^2=(a-b)^2+2ab\). Thus, \(a^2+b^2=5^2+2(6)=25+12=37\). Option B results from incorrectly adding only \(ab\) instead of \(2ab\). In exams, remember that \((a-b)^2=a^2-2ab+b^2\), which leads to this 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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