# Linear Quadratic Cubic Quartic

Algebra Level 3

$\begin{eqnarray} a \ \ + b \ + c \ \ &=& 2\\ a^{ 2 } + b^{ 2 } + c^{ 2 } &=& 6\\ a^{ 3 } + b^{ 3 } + c^{ 3 }&=& 8\\ \end{eqnarray}$ For complex numbers $$a,b,c$$, we are given the system of equations above. Find the value of $$a^{ 4 } + b^{ 4 } + c^{ 4 }$$.

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