$$a + b + c = 0 , a ^ { 2 } + b ^ { 2 } + c ^ { 2 } = 1 , a ^ { 4 } + b ^ { 4 } + c ^ { 4 } =$$
$a=-\left(b+c\right)\text{, }b=\frac{\sqrt{2-3c^{2}}-c}{2}\text{, }c\in \mathrm{C}\text{, }d=\left(b+c\right)^{4}+b^{4}+c^{4}$
$a=-\left(b+c\right)\text{, }b=\frac{-\sqrt{2-3c^{2}}-c}{2}\text{, }c\in \mathrm{C}\text{, }d=\left(b+c\right)^{4}+b^{4}+c^{4}$
$a=-\left(b+c\right)\text{, }b=\frac{\sqrt{2-3c^{2}}-c}{2}\text{, }c\in \begin{bmatrix}-\frac{\sqrt{6}}{3},\frac{\sqrt{6}}{3}\end{bmatrix}\text{, }d=\left(b+c\right)^{4}+b^{4}+c^{4}\text{; }a=-\left(b+c\right)\text{, }b=\frac{-\sqrt{2-3c^{2}}-c}{2}\text{, }c\in \begin{bmatrix}-\frac{\sqrt{6}}{3},\frac{\sqrt{6}}{3}\end{bmatrix}\text{, }d=\left(b+c\right)^{4}+b^{4}+c^{4}$
