# Never Judge a Problem by its Title

Algebra Level 5

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

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

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

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