Roots of polynomial equations

I was happily answering some questions from my further pure textbook earlier until I encountered the last question; forgive me in advance for my lack of understanding, I'm only a sixth form student at the moment and I don't have as much knowledge as most people on this site!

Here's the question:

*The roots of the equation $\displaystyle x^3 + ax + b$ are $\displaystyle \alpha, \beta, \gamma$. Find the equation with roots $\displaystyle \frac{\beta}{\gamma} + \frac{\gamma}{\beta}, \frac{\gamma}{\alpha} + \frac{\alpha}{\gamma}, \frac{\alpha}{\beta} + \frac{\beta}{\alpha}$.*

Initially I tried to use substitution but that failed epicly. Overall, I'm really confused - please could somebody assist me?

Also, on a side note, I'm new here! Just thought you'd like to know (Smile)