Solucionar x^3-3x^2+1=0

$${ x }^{ 3 } -3 { x }^{ 2 } +1=0$$

Resolver para x (solución compleja)

$$x=\frac{\sqrt[3]{2}\left(-1+\sqrt{3}i\right)^{-\frac{2}{3}}\left(e^{\frac{\pi i}{3}}\left(-1+\sqrt{3}i\right)^{\frac{4}{3}}+\left(2\left(-1+\sqrt{3}i\right)\right)^{\frac{2}{3}}+2\sqrt[3]{2}e^{-\frac{\pi i}{3}}\right)}{2}\approx -0,532088886-6,938893904 \cdot 10^{-17}i$$

$$x=\frac{2^{\frac{2}{3}}\left(1+\sqrt{3}i\right)^{-\frac{1}{3}}\left(\sqrt[3]{2\left(1+\sqrt{3}i\right)}+\left(1+\sqrt{3}i\right)^{\frac{2}{3}}+2^{\frac{2}{3}}\right)}{2}\approx 2,879385242+2,220446049 \cdot 10^{-16}i$$

$$x=\frac{\left(1+\sqrt{3}i\right)^{-\frac{4}{3}}\left(\sqrt[3]{2}\left(-\sqrt{3}\sqrt[3]{2}i\left(1+\sqrt{3}i\right)^{\frac{5}{3}}-\sqrt[3]{2}\left(1+\sqrt{3}i\right)^{\frac{5}{3}}-8\right)+4\left(1+\sqrt{3}i\right)^{\frac{4}{3}}\right)}{4}\approx 0,652703645+9,714451465 \cdot 10^{-17}i$$

Resolver para x

$$x=-2\cos(\frac{2\pi }{9})+1\approx -0,532088886$$

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

$$x=-2\sin(\frac{\pi }{18})+1\approx 0,652703645$$