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A student claims that if \(a+b+c=12\) and \(ab+bc+ca=35\), then \(a^2+b^2+c^2=74\). Which option about the student’s claim is correct?
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Answer and explanation
Correct answer: The claim is correct; the value is \(74\).
Using \((a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)\), we get \(a^2+b^2+c^2=12^2-2\times35=144-70=74\). Thus, the claim is correct. \(109\) results from forgetting the factor \(2\). Exam tip: always check the coefficient of mixed terms.
Frequently asked questions
What is the correct answer to this question?
The claim is correct; the value is \(74\).
Why is this the correct answer?
Using \((a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)\), we get \(a^2+b^2+c^2=12^2-2\times35=144-70=74\). Thus, the claim is correct. \(109\) results from forgetting the factor \(2\). Exam tip: always check the coefficient of mixed terms.
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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