# Not that complex

Algebra Level 3

Let the polynomial $$x^{2}+x+1$$ have roots $$\alpha$$ and $$\beta$$. Then there exists a polynomial with the roots $$\alpha^{2}$$ and $$\beta^{2}$$ in the form of $$ax^2+bx+c$$, where $$a$$, $$b$$ and $$c$$ are all integers, with $$a$$ begin positive and $$\gcd(a,b,c) = 1$$.

Find $$a+b+c$$.

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