# Maybe the roots are rational? I'll try that

Algebra Level 5

Let $p,q$ and $r$ be the roots of $f(x)=x^3+3x+8$. Suppose a monic cubic $g(x)$ has the roots

$\frac{p^2+q^2}{r^2}, \frac{p^2+r^2}{q^2}, \frac{q^2+r^2}{p^2}$

The value of $g(-1)$ is $\dfrac{a}{b}$ for relatively prime $a$ and $b$. Find $a+b$.

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