The fraction $\frac{1}{3}$ is not a decimal number. And we know

𝑎^{2} + 𝑏^{2} = 𝑐^{2} .

To solve the cubic equation $𝑡^{3} + 𝑝 𝑡 + 𝑞 = 0$ (where the real numbers $𝑝, 𝑞$ satisfy $4 𝑝^{3} + 27 𝑞^{2} > 0$ ) one can use Cardano's formula:

\sqrt[3]{- \frac{𝑞}{2} + \sqrt{\frac{𝑞^{2}}{4} + \frac{𝑝^{3}}{27}}} + \sqrt[3]{- \frac{𝑞}{2} - \sqrt{\frac{𝑞^{2}}{4} + \frac{𝑝^{3}}{27}}} .

For any $𝑢_{1}, \dots, 𝑢_{𝑛} \in ℂ$ and $𝑣_{1}, \dots, 𝑣_{𝑛} \in ℂ$ , the Cauchy-Bunyakovsky-Schwarz inequality can be written as follows:

\begin{matrix} {| \sum_{𝑘 = 1}^{𝑛} 𝑢_{𝑘} \bar{𝑣_{𝑘}} |}^{2} \leq {(\sum_{𝑘 = 1}^{𝑛} | 𝑢_{𝑘} |)}^{2} {(\sum_{𝑘 = 1}^{𝑛} | 𝑣_{𝑘} |)}^{2} . \end{matrix}