# Bashing unavailable - part 2

Algebra Level 4

$\large{ \begin{cases} a+b+c=1 \\ a^2+b^2+c^2 = 2 \\ a^3 + b^3+c^3 = 3 \\ \end{cases} }$

Let $$a,b$$ and $$c$$ satisfy the system of equations above.

Given that $$a^4 + b^4 + c^4 = \dfrac{a_1}{a_2}$$ for coprime positive integers $$a_1$$ and $$a_2$$. And $$a^5 + b^5 + c^5 = a_3$$.

Find the value of $$a_1 + a_2 + a_3$$.

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