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If (\alpha=3+\sqrt{11}) and (\beta=3-\sqrt{11}), what is (\alpha^2+\beta^2)?
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Answer and explanation
Correct answer: (40)
(\alpha+\beta=6) and (\alpha\beta=9-11=-2), so (\alpha^2+\beta^2=36-2(-2)=40). The identity (\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha\beta) is useful.
Frequently asked questions
What is the correct answer to this question?
(40)
Why is this the correct answer?
(\alpha+\beta=6) and (\alpha\beta=9-11=-2), so (\alpha^2+\beta^2=36-2(-2)=40). The identity (\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha\beta) is useful.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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