Solve the following equation:

$$
\sqrt[3]{(a+x)^{2}}+20 \sqrt[3]{(a-x)^{2}}=9 \sqrt[3]{a^{2}-x^{2}}
$$
Divide every term of the equation by $\sqrt[3]{(a+x)^{2}}$:

$$
20 \sqrt[3]{\left(\frac{a-x}{a+x}\right)^{2}}-9 \sqrt[3]{\frac{a-x}{a+x}}+1=0
$$

from which

$$
\sqrt[3]{\frac{a-x}{a+x}}=\frac{9 \pm 1}{40}
$$

from which

$$
x_{1}=\frac{63}{65} a, x_{2}=\frac{62}{63} a
$$

(Mihály Dolowschiák, Györ.)

The problem was also solved by: Bayer B., Bobál S., Boros J., Csete A., Filkorn J., Freibauer E., Glass M., Grosz K., Jankovich S., Juvancz I., Kárf J., Kiss A., Kohn B., Kornis Ö., Krausz B., Krisztián Gy., Kürth A., Mandel M., Perl Gy., Petrogalli G., Pollák N., Porkoláb J., Rehberger Z., Sasvári G., Sasvári J., Schmidt B., Spitzer Ö., Tinyó J., Weigl. G., Weisz J.