If $\alpha$ and $\beta$ are the roots of $2x^2 - 6x + 3 = 0$, what is $\frac{\alpha}{\beta} + \frac{\beta}{\alpha}$?

Explanation

1. 01

   $\alpha + \beta = \frac{6}{2} = 3$ and $\alpha\beta = \frac{3}{2}$.

2. 02

   $\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = \frac{\alpha^2 + \beta^2}{\alpha\beta}$.

3. 03

   $\alpha^2 + \beta^2 = 9 - 2 \times \frac{3}{2} = 6$.

4. 04

   So the value is $\frac{6}{3/2} = 4$.