Určení kořenů binomické rovnice
Urči kořeny binomické rovnice za použití rozkladu na součin mnohočlenů nebo substituce:
\large x^6-729 = 0
\large K =\left \{ -3;3;- \Large \frac{3}{2}\large +\Large \frac{2\sqrt {3}}{2}\large \text{i};- \Large \frac{3}{2}\large -\Large \frac{2\sqrt {3}}{2}\large \text{i};\Large \frac{3}{2}\large -\Large \frac{2\sqrt {3}}{2}\large \text{i};\Large \frac{3}{2}\large +\Large \frac{2\sqrt {3}}{2}\large \text{i}\right \}
\large K =\left \{ -3;3;- \Large \frac{3}{2}\large +\Large \frac{3\sqrt {3}}{2}\large \text{i};- \Large \frac{3}{2}\large -\Large \frac{3\sqrt {3}}{2}\large \text{i};\Large \frac{3}{2}\large -\Large \frac{3\sqrt {3}}{2}\large \text{i};\Large \frac{3}{2}\large +\Large \frac{3\sqrt {3}}{2}\large \text{i}\right \}
\large K =\left \{ -3;3;- \Large \frac{3}{2}\large +\Large \frac{3\sqrt {2}}{2}\large \text{i};- \Large \frac{3}{2}\large -\Large \frac{3\sqrt {2}}{2}\large \text{i};\Large \frac{3}{2}\large -\Large \frac{3\sqrt {2}}{2}\large \text{i};\Large \frac{3}{2}\large +\Large \frac{3\sqrt {2}}{2}\large \text{i}\right \}
\large K =\left \{ -3;3;- \Large \frac{3}{2}\large +\Large \frac{3\sqrt {3}}{3}\large \text{i};- \Large \frac{3}{2}\large -\Large \frac{3\sqrt {3}}{3}\large \text{i};\Large \frac{3}{2}\large -\Large \frac{3\sqrt {3}}{3}\large \text{i};\Large \frac{3}{2}\large +\Large \frac{3\sqrt {3}}{3}\large \text{i}\right \}