Linear Quadratic Cubic Quartic

Algebra Level 3

a  +b +c  =2a2+b2+c2=6a3+b3+c3=8 \begin{aligned} a \ \ + b \ + c \ \ &=& 2\\ a^{ 2 } + b^{ 2 } + c^{ 2 } &=& 6\\ a^{ 3 } + b^{ 3 } + c^{ 3 }&=& 8\\ \end{aligned} For complex numbers a,b,ca,b,c, we are given the system of equations above. Find the value of a4+b4+c4 a^{ 4 } + b^{ 4 } + c^{ 4 } .

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