求解 x^3-8x+16=0

$$x ^ { 3 } - 8 x + 16 = 0$$

求解 x 的值 (复数求解)

$$x=-\frac{9^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(-\sqrt{3}\sqrt[3]{\sqrt{57}-9}i-\sqrt[3]{\sqrt{57}-9}+2\sqrt[3]{-\sqrt{57}-9}\right)}{18}\approx 0.136818325-2.121994931i$$

$$x=\frac{2\times 9^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{57}-9}+\sqrt[3]{-\sqrt{57}-9}\right)}{9}\approx 1.769292354+3.064504251i$$

$$x=-\frac{9^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{\sqrt{57}-9}+2\sqrt[3]{-\sqrt{57}-9}+\sqrt{3}\sqrt[3]{\sqrt{57}-9}i\right)}{18}\approx -1.906110679-0.94250932i$$

求解 x 的值

$$x = -\frac{2 \cdot 9 ^ {\frac{2}{3}} {(\sqrt[3]{\sqrt{57} + 9} + \sqrt[3]{9 - \sqrt{57}})}}{9} \approx -3.538584708$$