Question

If $p+q=5$ and $pq=6$, then $p^3+q^3=?$

Answer 1

Compute the required value:

It is given that $p+q=5,pq=6$

Using the identity ${\left(a+b\right)}^3=a^3+b^3+3ab\left(a+b\right)$

$\begin{array}{rcl}& \Rightarrow & {\left(p+q\right)}^3=p^3+q^3+3pq\left(p+q\right)\\ & \Rightarrow & {\left(5\right)}^3=p^3+q^3+\left(3\times 6\right)\times \left(5\right)\\ & \Rightarrow & 125=p^3+q^3+90\\ & \Rightarrow & p^3+q^3=125-90\\ & \Rightarrow & p^3+q^3=35\end{array}$

Hence the value of $p^3+q^3$ is $35$.