If (\alpha=1+\sqrt{2}) and (\beta=1-\sqrt{2}), what is (\alpha^3+\beta^3)?

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Answer and explanation

Correct answer: (14)

(\alpha+\beta=2) and (\alpha\beta=-1), so (\alpha^3+\beta^3=2^3-3(-1)(2)=14). Use (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\alpha+\beta)).

What is the correct answer to this question?

(14)

Why is this the correct answer?

(\alpha+\beta=2) and (\alpha\beta=-1), so (\alpha^3+\beta^3=2^3-3(-1)(2)=14). Use (\alpha^3+\beta^3=(\alpha+\beta)^3-3\alpha\beta(\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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