If \(m+n=11\) and \(mn=24\), what is the value of \(m^2+n^2\)?
Answer and explanation
Correct answer: 73
Use the identity \(m^2+n^2=(m+n)^2-2mn\). Thus, \(m^2+n^2=11^2-2(24)=121-48=73\). Option B results from subtracting \(mn\) only once, whereas the identity requires subtracting \(2mn\). In an exam, writing the relevant algebraic identity first is the quickest method.
Frequently asked questions
What is the correct answer to this question?
73
Why is this the correct answer?
Use the identity \(m^2+n^2=(m+n)^2-2mn\). Thus, \(m^2+n^2=11^2-2(24)=121-48=73\). Option B results from subtracting \(mn\) only once, whereas the identity requires subtracting \(2mn\). In an exam, writing the relevant algebraic identity first is the quickest method.
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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