A Cubic Polynomial Transformed

Algebra Level 4

The Roots of the following Cubic Equation are α\displaystyle \alpha, β\displaystyle \beta and γ\displaystyle \gamma.

x3+7x2+2x+9=0\displaystyle x^3+7x^2+2x+9=0

Then the value of the Expression

(3α2)(3β2)(3γ2)(2+3α)(2+3β)(2+3γ)\displaystyle \dfrac{(3 \alpha-2)(3 \beta-2)(3 \gamma-2)}{(2+3 \alpha)(2+3 \beta)(2+3 \gamma)}

Can be written as ab\displaystyle \dfrac{a}{b}, where a\displaystyle a and b\displaystyle b are coprime positive integers. Find a+b\displaystyle a+b.


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