Quadratic Equation #9

Algebra Level 3

Let equation ax2+bx+c=0ax^{2} + bx + c = 0 whose roots are the reciprocals of the roots of x2+2x+3=0.x^{2} + 2x +3 = 0.

If a,b,c a, b, c are positive integers such that gcd(a,b,c)=1 \gcd (a, b, c) = 1 , find a+b+c. a + b + c.

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