Rozwiąż x^3-3x+1=0

$$x ^ { 3 } - 3 x + 1 = 0$$

Rozwiąż względem x (complex solution)

$$x=\frac{\sqrt[3]{2}\left(-1+\sqrt{3}i\right)^{-\frac{4}{3}}\left(\sqrt[3]{2}\left(-1+\sqrt{3}i\right)^{\frac{8}{3}}+8\right)}{4}\approx -1,879385242$$

$$x=\frac{2^{\frac{2}{3}}\left(-1+\sqrt{3}i\right)^{-\frac{1}{3}}\left(\left(-1+\sqrt{3}i\right)^{\frac{2}{3}}+2^{\frac{2}{3}}\right)}{2}\approx 1,532088886+2,220446049 \cdot 10^{-16}i$$

$$x=\frac{\sqrt[3]{2}\left(1+\sqrt{3}i\right)^{-\frac{2}{3}}\left(\left(1+\sqrt{3}i\right)^{\frac{4}{3}}+2^{\frac{4}{3}}\right)}{2}\approx 1,532088886-2,220446049 \cdot 10^{-16}i$$

Rozwiąż względem x

$$x=-2\cos(\frac{\pi }{9})\approx -1,879385242$$

$$x=2\cos(\frac{2\pi }{9})\approx 1,532088886$$

$$x=2\sin(\frac{\pi }{18})\approx 0,347296355$$