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If (\alpha=5+\sqrt{6}) and (\beta=5-\sqrt{6}), what is the value of (\alpha^2+\beta^2)?
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Answer and explanation
Correct answer: (62)
(\alpha+\beta=10) and (\alpha\beta=25-6=19), so (\alpha^2+\beta^2=100-38=62). Use (\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha\beta).
Frequently asked questions
What is the correct answer to this question?
(62)
Why is this the correct answer?
(\alpha+\beta=10) and (\alpha\beta=25-6=19), so (\alpha^2+\beta^2=100-38=62). Use (\alpha^2+\beta^2=(\alpha+\beta)^2-2\alpha\beta).
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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