Řešení kubické rovnice v komplexních číslech
Řeš v \mathbb{C} rovnici:
\large 27x^3+125 = 0
\large K = \left \{-\Large \frac{5}{3}\large ;\Large \frac{5}{6}\large -\Large \frac{5\sqrt {3}}{5}\large \text{i};\Large \frac{5}{6}\large +\Large \frac{5\sqrt {3}}{5}\large \text{i}\right \}
\large K = \left \{-\Large \frac{5}{3}\large ;\Large \frac{5}{6}\large -\Large \frac{5\sqrt {3}}{6}\large \text{i};\Large \frac{5}{6}\large +\Large \frac{5\sqrt {3}}{6}\large \text{i}\right \}
\large K = \left \{-\Large \frac{5}{3}\large ;\Large \frac{5}{6}\large -\Large \frac{5\sqrt {2}}{6}\large \text{i};\Large \frac{5}{6}\large +\Large \frac{5\sqrt {2}}{6}\large \text{i}\right \}
\large K = \left \{-\Large \frac{5}{3}\large ;\Large \frac{5}{6}\large -\Large \frac{4\sqrt {3}}{6}\large \text{i};\Large \frac{5}{6}\large +\Large \frac{4\sqrt {3}}{6}\large \text{i}\right \}