If (\alpha=4+\sqrt{15}) and (\beta=4-\sqrt{15}), what is the value of (\frac{\alpha}{\beta}+\frac{\beta}{\alpha})?

(62)

Here (\alpha+\beta=8) and (\alpha\beta=1), so (\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{64-2}{1}=62). In such questions, first find the sum and product.

This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.