\left\{ \begin{array} { l } { a ^ { 3 } + a + 1 = 0 } \\ { a ^ { 4 } = b } \end{array} \right.
Solve for a, b
a=\frac{18^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{93}-9}-\sqrt[3]{\sqrt{93}+9}\right)}{18}\approx -0.682327804
b=\frac{18^{\frac{2}{3}}\left(-4\sqrt[3]{12}\left(\sqrt{93}+9\right)^{\frac{2}{3}}-4\sqrt[3]{12}\left(\sqrt{93}-9\right)^{\frac{2}{3}}+\left(\sqrt{93}+9\right)^{\frac{4}{3}}+\left(\sqrt{93}-9\right)^{\frac{4}{3}}+6\times 12^{\frac{2}{3}}\right)}{324}\approx 0.216756572
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