If \(m+n=9\) and \(mn=18\), what is the value of \(m^2+n^2\)?
Answer and explanation
Correct answer: 45
Use the identity \(m^2+n^2=(m+n)^2-2mn\). Thus, \(m^2+n^2=9^2-2(18)=81-36=45\), so the correct answer is 45. The option 63 may result from an incorrect calculation while subtracting \(2mn\). Exam tip: remember the identity \(a^2+b^2=(a+b)^2-2ab\) for such questions.
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
Use the identity \(m^2+n^2=(m+n)^2-2mn\). Thus, \(m^2+n^2=9^2-2(18)=81-36=45\), so the correct answer is 45. The option 63 may result from an incorrect calculation while subtracting \(2mn\). Exam tip: remember the identity \(a^2+b^2=(a+b)^2-2ab\) for such questions.
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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