In the equation $\mathrm{Az} x^{2}+p x+12=0$, determine $p$ such that $x_{1}-x_{2}=1$.

(Note: The term $\mathrm{Az}$ is kept as is, as it might be a specific notation or coefficient in the context of the problem.)
According to the problem,

$$
\frac{-p+\sqrt{p^{2}-48}}{2}-\frac{-p-\sqrt{p^{2}-48}}{2}=\sqrt{p^{2}-48}=1
$$

from which

$$
p^{2}=49, \quad \text { or } \quad p= \pm 7
$$

(Bauer Elemér, Budapest, V. district high school)

The problem was also solved by: Barok I., Bayer N., Bendl K., Breuer P., Cukor G., Csada I., Ehrenfeld N., Engler J., Fried E., Füstös P., Grossberger Z., Grün E., Kiss J., Kirchknopf E., Koffler B., Kovács Gy., Miklóssy K., Neumann L., Rosenthal M., Sebestyén I., Szécsi I., Szilárd V., Szőke D., Tasch N., Tóth B., Viola R., Wáhl V., Wellis D.