Résoudre x^3+x^2+1=6

$$x ^ { 3 } + x ^ { 2 } + 1 = 6$$

Calculer x (solution complexe)

$$x=-\frac{2^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(-\sqrt[3]{3\left(9\sqrt{655}+133\sqrt{3}\right)}i-\sqrt{3}\sqrt[3]{2}i-\sqrt[3]{3\sqrt{1965}+133}+2\sqrt[3]{133-3\sqrt{1965}}+\sqrt[3]{2}\right)}{24}\approx -1,216713832+1,416950946i$$

$$x = \frac{2 ^ {\frac{2}{3}} {(\sqrt[3]{3 \sqrt{1965} + 133} + \sqrt[3]{133 - 3 \sqrt{1965}} - \sqrt[3]{2})}}{6} \approx 1,433427664$$

$$x=-\frac{2^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{3\sqrt{1965}+133}+2\sqrt[3]{133-3\sqrt{1965}}+\sqrt[3]{2}+\sqrt[3]{3\left(9\sqrt{655}+133\sqrt{3}\right)}i+\sqrt{3}\sqrt[3]{2}i\right)}{24}\approx -1,216713832-1,416950946i$$

Calculer x

$$x = \frac{2 ^ {\frac{2}{3}} {(\sqrt[3]{3 \sqrt{1965} + 133} + \sqrt[3]{133 - 3 \sqrt{1965}} - \sqrt[3]{2})}}{6} \approx 1,433427664$$