Bashing unavailable - part 1

Algebra Level 4

Given that a+b+c=1a2+b2+c2=2a3+b3+c3=3.\color{#20A900}{a+b+c =1} \\ \color{#3D99F6}{a^2+b^2+c^2=2} \\ \color{#D61F06}{a^3+b^3+c^3=3}. If a4+b4+c4=a1a2a^4+b^4+c^4= \frac{a_1}{a_2} where a1a_1, a2a_2 are positive coprime integers, then find a1+a2a_1+a_2.

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