[Math] How to find the sum of the cubes of the roots in a cubic polynomial

Question

I have an equation, $x^3-x^2+x-2$, with three distinct roots, $p$, $q$ and $r$. What is the value of $p^3+q^3+r^3$?

I'm not sure how to do this. Using Vieta's formula, we know that:
$pqr= 2$

$pq+pr+qr= 1$

$p+q+r= 1$

After this, what should I do?

Answer 1

Try expanding $(p+q+r)^3$ and $(pq+pr+qr)(p+q+r)$ and see if anything comes to mind. You should be able to retrieve $p^3+q^3+r^3$ from there.