Résoudre (x^4+2x-3x^2)=(x^2-1)

$$( x ^ { 4 } + 2 x - 3 x ^ { 2 } ) = ( x ^ { 2 } - 1 )$$

Calculer x (solution complexe)

$$x=\frac{\sqrt{3}i\sqrt[3]{-1+3\sqrt{111}i}}{6}-\frac{5\sqrt{3}i\left(-1+3\sqrt{111}i\right)^{-\frac{1}{3}}}{3}-\frac{\sqrt[3]{-1+3\sqrt{111}i}}{6}-\frac{5\left(-1+3\sqrt{111}i\right)^{-\frac{1}{3}}}{3}-\frac{1}{3}\approx -2,170086487-5,551115123 \cdot 10^{-17}i$$

$$x=\frac{\sqrt[3]{-1+3\sqrt{111}i}+10\left(-1+3\sqrt{111}i\right)^{-\frac{1}{3}}-1}{3}\approx 1,481194304-7,401486831 \cdot 10^{-17}i$$

$$x=-\frac{\sqrt{3}i\sqrt[3]{-1+3\sqrt{111}i}}{6}+\frac{5\sqrt{3}i\left(-1+3\sqrt{111}i\right)^{-\frac{1}{3}}}{3}-\frac{\sqrt[3]{-1+3\sqrt{111}i}}{6}-\frac{5\left(-1+3\sqrt{111}i\right)^{-\frac{1}{3}}}{3}-\frac{1}{3}\approx -0,311107817+1,665334537 \cdot 10^{-16}i$$

$$x=1$$

Calculer x

$$x=\frac{-2\sqrt{10}\cos(\frac{\arccos(\frac{\sqrt{10}}{100})}{3})-1}{3}\approx -2,170086487$$

$$x=\frac{\sqrt{10}\left(\sqrt{3}\sin(\frac{\arccos(\frac{\sqrt{10}}{100})}{3})+\cos(\frac{\arccos(\frac{\sqrt{10}}{100})}{3})\right)-1}{3}\approx 1,481194304$$

$$x=\frac{\sqrt{10}\left(-\sqrt{3}\sin(\frac{\arccos(\frac{\sqrt{10}}{100})}{3})+\cos(\frac{\arccos(\frac{\sqrt{10}}{100})}{3})\right)-1}{3}\approx -0,311107817$$

$$x=1$$