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Question Number 192898 by Red1ight last updated on 30/May/23

$$\mathrm{Solve}\mathrm{for}x$$$$x^3-7x-2=0$$

Commented by Frix last updated on 30/May/23

$$\mathrm{You}\mathrm{need}\mathrm{the}TrigonometricSolution\mathrm{to}$$$$\mathrm{get}\mathrm{exact}\mathrm{solutions}:$$$$x_1=-\frac{2\sqrt{21}}{3}\cos \frac{\pi +{2\sin }^{-1}\frac{3\sqrt{21}}{49}}{6}\approx -2.48928857$$$$x_2=-\frac{2\sqrt{21}}{3}\sin \frac{{\sin }^{-1}\frac{3\sqrt{21}}{49}}{3}\approx -.289168535$$$$x_3=\frac{2\sqrt{21}}{3}\sin \frac{\pi +{\sin }^{-1}\frac{3\sqrt{21}}{49}}{3}\approx 2.77845712$$

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