Given that x+y=13 and xy=-24, find the distance from the point (x,y) to the origin.
We are trying to find \(\sqrt{x^2 + y^2}\).
Simplify as follows:
\(\sqrt{(x+y)^2 - 2xy}\)
\(\sqrt{13^2 -( 2 \times -24)}\)
\(\sqrt{169 - - 48}\)
\(\sqrt{169 + 48}\)
\(\color{brown}\boxed{\sqrt{217}}\)