Finding $x^3+y^3$, given $x + y = 5$ and $xy = 1$ 
Given
$$x + y = 5 \qquad xy = 1$$
Find $x^3 + y^3$.

To solve this, I tried this:
$y = \frac{1} {x}$
$x + \frac{1}{x} = 5$
$x^2 - 5x + 1 = 0$
What formula needs to be used to find the value of $x$?

$$
\begin{aligned}
x^3+y^3 & =(x+y)^3-3 x y(x+y) \\
& =5^3-3(1)(5) \\
& =110
\end{aligned}
$$
