Solve the following system of equations:

$$
\begin{array}{r}
x^{4}+y^{4}=272 \\
x+y=6
\end{array}
$$
Raising (2) to the square and taking into account (1), we get:

$$
2 x^{3} y+3 x^{2} y^{2}+2 x y^{3}=512
$$

or

$$
x y\left[2(x+y)^{2}-x y\right]=512
$$

or

$$
(x y)^{2}-72 x y+512=0,
$$

from which

$$
\begin{gathered}
x y=64 \\
x^{\prime} y^{\prime}=8
\end{gathered}
$$

Connecting these equations with (2), we obtain:

$$
x_{1}=y_{2}=2, x_{2}=y_{1}=4, x_{3}=y_{4}=3+i \sqrt{55}, x_{4}=y_{3}=3-i \sqrt{55}
$$

(Klein Adolf, Székesfehérvár.)