x^3+x^2+1=0 ઉકેલો

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

x માટે ઉકેલો (જટિલ સમાધાન)

$$x=-\frac{2^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(-\sqrt{3}\sqrt[3]{3\sqrt{93}-29}i-\sqrt{3}\sqrt[3]{2}i-\sqrt[3]{3\sqrt{93}-29}+2\sqrt[3]{-3\sqrt{93}-29}+\sqrt[3]{2}\right)}{24}\approx 0.069977351-0.886549388i$$

$$x=\frac{2^{\frac{2}{3}}\left(\sqrt[3]{3\sqrt{93}-29}+\sqrt[3]{-3\sqrt{93}-29}-\sqrt[3]{2}\right)}{6}\approx 0.232785616+0.980546783i$$

$$x=-\frac{2^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{3\sqrt{93}-29}+2\sqrt[3]{-3\sqrt{93}-29}+\sqrt[3]{2}+\sqrt{3}\sqrt[3]{3\sqrt{93}-29}i+\sqrt{3}\sqrt[3]{2}i\right)}{24}\approx -1.302762967-0.093997395i$$

x માટે ઉકેલો

$$x=-\frac{2^{\frac{2}{3}}\sqrt[3]{3\sqrt{93}+29}}{6}-\frac{2^{\frac{2}{3}}\sqrt[3]{29-3\sqrt{93}}}{6}-\frac{1}{3}\approx -1.465571232$$