394. Solve the equation: $x^{6}-19 x^{3}=216$.

## Lambert's Problems.

From "Beiträge zur Mathematik ${ }^{4}$.

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394. Let

$$
x^{3}=z, z-19 z-216=0
$$

Maclaurin's solution:

$$
\begin{gathered}
z^{2}-19 z+\frac{361}{4}=216+\frac{361}{4}=\frac{1225}{4} \\
z-\frac{19}{2}= \pm \frac{35}{2} ; z=\frac{19 \pm 35}{2}=27 \text { or }-8
\end{gathered}
$$

therefore, $x(=\sqrt[3]{z})$ equals 3 or -2.

Johann Heinrich Lambert (1728-1777), a distinguished German mathematician, a member of the Berlin and Munich academies, a profound expert in geometry, who worked on the investigation of the properties of conic sections and the theory of perspective. Science owes him the proof of the irrationality of the number $\pi$.