# A Too Easy One in Fact!

Algebra Level 4

Let $$\alpha$$ and $$\beta$$ be the roots of the quadratic equation $$x^2+x+1 = 0$$. If $$a,b$$ and $$c$$ are positive integers satisfying $$\gcd(a,b,c) = 22$$ such that the quadratic equation $$ax^2+bx+ c=0$$ has $$\alpha^{62}$$ and $$\beta^{62}$$ as its roots, find the value of $$a+b+c$$.

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