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Algebra Level 5

Let P\displaystyle P and Q\displaystyle Q be two quadratic polynomials, such that P(z)=3z2+4z+3\displaystyle P(z)=3z^2+4z+3 and Q(z)=3z2+6z+15\displaystyle Q(z)=3z^2+6z+15.

Furthermore, the product of P(x)\displaystyle P(x) and Q(y)\displaystyle Q(y) for some x,yR\displaystyle x,y \in \mathbb{R} is 20\displaystyle 20. Find their sum, ie, P(x)+Q(y)\displaystyle P(x)+Q(y).

It can be expressed as ab\displaystyle \dfrac{a}{b} for coprime positive integers a\displaystyle a and b\displaystyle b. Find a+b\displaystyle a+b.

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