If ( (x+y)^2=81 ) and (xy=14), what is the value of (x^2+y^2)?
Answer and explanation
Correct answer: 53
Using the identity \((x+y)^2=x^2+y^2+2xy\), we get \(x^2+y^2=(x+y)^2-2xy\). Therefore, \(x^2+y^2=81-2(14)=81-28=53\). Hence, 53 is the correct answer. A common error leading to 67 is subtracting only \(xy\) instead of \(2xy\). Exam tip: always account for the \(2xy\) term when finding the sum of squares.
Frequently asked questions
What is the correct answer to this question?
53
Why is this the correct answer?
Using the identity \((x+y)^2=x^2+y^2+2xy\), we get \(x^2+y^2=(x+y)^2-2xy\). Therefore, \(x^2+y^2=81-2(14)=81-28=53\). Hence, 53 is the correct answer. A common error leading to 67 is subtracting only \(xy\) instead of \(2xy\). Exam tip: always account for the \(2xy\) term when finding the sum of squares.
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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