What's f(4)f(4)?

Algebra Level 4

{a+b+c=0a3+b3+c3=3a5+b5+c5=10\large \begin{cases} a+b+c=0 \\ a^{3}+b^{3}+c^{3}=3 \\ a^{5}+b^{5}+c^{5}=10 \end{cases}

If aa, bb and cc are real numbers satisfying the system of equations above, find a4+b4+c4 a^4 + b^4 + c^4 .

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