# Three Math Problems Joined Into One

Algebra Level 3

$\large (x^2+5x+6)^{2x^2-x-1} = 1$

Given that $$Ax^2 + Bx + C = 0$$ is a quadratic equation whose two roots (of $$x$$) are the reciprocal of the values of $$x$$ that satisfy the exponential equation above. And if the greatest common divisor of $$A,B,C$$ equals to 1, find the value of $$A+B+C$$.

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