求解 y=x^3+6x

$$y = x ^ { 3 } + 6 x$$

求解 x 的值 (复数求解)

$$x=\frac{2^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(\sqrt{y^{2}+32}+y\right)^{-\frac{1}{3}}\left(\left(1+\sqrt{3}i\right)\left(\sqrt{y^{2}+32}+y\right)^{\frac{2}{3}}+4\times 2^{\frac{2}{3}}\right)}{8}$$

$$x=\frac{2^{\frac{2}{3}}\left(\sqrt{y^{2}+32}+y\right)^{-\frac{1}{3}}\left(\left(\sqrt{y^{2}+32}+y\right)^{\frac{2}{3}}-2\times 2^{\frac{2}{3}}\right)}{2}$$

$$x=-\frac{2^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(\sqrt{y^{2}+32}+y\right)^{-\frac{1}{3}}\left(\left(-1+\sqrt{3}i\right)\left(\sqrt{y^{2}+32}+y\right)^{\frac{2}{3}}-4\times 2^{\frac{2}{3}}\right)}{8}$$

求解 x 的值

$$x=\frac{2^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{y^{2}+32}+y}+\sqrt[3]{-\sqrt{y^{2}+32}+y}\right)}{2}$$

求解 y 的值

$$y=x\left(x^{2}+6\right)$$