350. Solve the equation:

$$
y^{6}+2 b^{3} y^{3}=a^{6}
$$

## Bombelli's Problems.
350. We assume:

$$
y^{3}=z ; z^{3}+2 b^{3} z-a^{6}=0 ; \quad z=-b^{3} \pm \sqrt{b^{6}+a^{6}}
$$

Knowing $z_{1}$ and $z_{2}$, we obtain two cubic binomial equations:

$$
y^{3}=z_{1} ; y^{3}=z_{2}
$$

Rafael Bombelli (1530-?), an Italian mathematician, author of the treatise on algebra (in Italian) "L'algebra parte maggiore dell'Aritmetica divisa in tre libri" (1572). In this work, a clear understanding of the significance of imaginary quantities is first evident. Additionally, Bombelli significantly improved algebraic notation.