Question

If $p+q=12$ and $pq=27$, then find the value of $p^3+q^3$.

Answer 1

Given $p+q=12$.
On cubing both sides, we get
$(p+q{)}^3=(12{)}^3$
$p^3+q^3+3pq(p+q)=1728$
$p^3+q^3+3\times 27\left(12\right)=1728$
$p^3+q^3+972=1728$
$p^3+q^3=1728-972$
$p^3+q^3=756$.