301. The sum of the squares of two numbers is 20, and their product is 8. Find these numbers.

## Problems by G. Schreiber (Grammateus).
301. Paciolo's Solution. Let the sum of the numbers $u$ and $y$ be $x$, and their difference $y$, where $x$ and $y$ are the unknowns. Then:

$$
x^{2}+y^{2}=2\left(u^{2}+v^{2}\right)
$$

and

$$
\begin{gathered}
x y=u^{2}-v^{2} \\
u^{2}+v^{2}=10
\end{gathered}
$$

And

$$
u^{2}-v^{2}=8
$$

from which

$$
u^{2}=9 \text { and } u=3 ; v^{2}=1 \text { and } v=1,
$$

therefore,

$$
x=4 ; y=2
$$

Heinrich Schreyber (Grammateus) from Erfurt (died in 1525), a mathematics teacher at the University of Vienna, author of the work “Rechentuch” (1518).