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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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