13. Given that $x+y=12$ and $x y=50$, find the exact value of $x^{2}+y^{2}$.
13. Answer: 44
Use the identity $x^{2}+y^{2}=(x+y)^{2}-2 x y=144-100=44$.
(Note: In this case, one may not be able to obtain the answer by guess-and-check; the values of $x$ and $y$ are not even real numbers)