Solve the following equation:

$12 x^{-\frac{3}{4}}-x^{-\frac{3}{8}}=2^{-4}$.
Let $x^{-\frac{3}{8}}=y$, then

$$
12 y^{2}-y=2^{-4},
$$

from which

$$
y_{1}=\frac{1}{8} \quad \text { and } \quad y_{2}=-\frac{1}{24}
$$

so

$$
x_{1}^{-\frac{3}{8}}=\frac{1}{8}, \quad \text { that is } \quad x_{1}=2^{8}=256
$$

and

$$
x_{2}^{-\frac{3}{8}}=-\frac{1}{24}, \quad \text { that is } \quad x_{4}=24 \frac{8}{3}=2304 \sqrt[3]{9}
$$

(Wáhl Viktor, Eger.)

The problem was also solved by: Babocsai Gy., Bauer E., Bayer N., Cukor G., Csada I., Ehrenfeld N., Füstös P., Grossberger Z., Kirchknopf E., Kiss J., Koffler B., Kovács Gy., Paunz A., Petrik S., Sárközy P., Sebestyén I., Tasch N., Tóth B.