$$
\left(\sqrt[3]{9-\sqrt{17}}-\sqrt[3]{\frac{1}{8} \sqrt{17}-1 \frac{1}{8}}\right) \cdot \sqrt[3]{3+\frac{1}{3} \sqrt{17}}=?
$$
The given expression can be written as:

$$
\begin{gathered}
\left(\sqrt[3]{9-\sqrt{17}}+\frac{1}{2} \sqrt[3]{9-\sqrt{17}}\right) \cdot \sqrt[3]{\frac{9+\sqrt{17}}{3}}= \\
=\frac{3}{2} \sqrt[3]{9-\sqrt{17}} \cdot \sqrt[3]{\frac{9+\sqrt{17}}{3}}=\frac{3}{2} \sqrt[3]{\frac{64}{3}}=6 \cdot \sqrt[3]{\frac{1}{3}}=6 \cdot \sqrt[3]{\frac{9}{27}}=2 \cdot \sqrt[3]{9}
\end{gathered}
$$

(László Bánó, Budapest.)

Number of solutions: 38.