求解 x^3-4x+7=0

$$x ^ { 3 } - 4 x + 7 = 0$$

求解 x 的值 (复数求解)

$$x=-\frac{18^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(-\sqrt{3}\sqrt[3]{\sqrt{3201}-63}i-\sqrt[3]{\sqrt{3201}-63}+2\sqrt[3]{-\sqrt{3201}-63}\right)}{72}\approx 0.230657336-1.628006528i$$

$$x=\frac{18^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{3201}-63}+\sqrt[3]{-\sqrt{3201}-63}\right)}{18}\approx 1.294566343+2.242254679i$$

$$x=-\frac{18^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{\sqrt{3201}-63}+2\sqrt[3]{-\sqrt{3201}-63}+\sqrt{3}\sqrt[3]{\sqrt{3201}-63}i\right)}{72}\approx -1.525223679-0.614248151i$$

求解 x 的值

$$x = -\frac{18 ^ {\frac{2}{3}} {(\sqrt[3]{\sqrt{3201} + 63} + \sqrt[3]{63 - \sqrt{3201}})}}{18} \approx -2.589132685$$