Risolvi x^2+1+1/x=0

$${ x }^{ 2 } +1+ \frac{ 1 }{ x } =0$$

Trova x (soluzione complessa)

$$x=\frac{18^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(2\sqrt[3]{\sqrt{93}+9}+\sqrt[3]{\sqrt{93}-9}+\sqrt[3]{9\left(\sqrt{31}-3\sqrt{3}\right)}i\right)}{72}\approx 0,341163902+1,1615414i$$

$$x=\frac{18^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{93}-9}-\sqrt[3]{\sqrt{93}+9}\right)}{18}\approx -0,682327804$$

$$x=\frac{18^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{9\left(\sqrt{31}-3\sqrt{3}\right)}i+2\sqrt[3]{\sqrt{93}+9}+\sqrt[3]{\sqrt{93}-9}\right)}{72}\approx 0,341163902-1,1615414i$$

Trova x

$$x=\frac{18^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{93}-9}-\sqrt[3]{\sqrt{93}+9}\right)}{18}\approx -0,682327804$$