Maybe the roots are rational? I'll try that

Algebra Level 5

Let p,qp,q and rr be the roots of f(x)=x3+3x+8f(x)=x^3+3x+8. Suppose a monic cubic g(x)g(x) has the roots

p2+q2r2,p2+r2q2,q2+r2p2\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)g(-1) is ab\dfrac{a}{b} for relatively prime aa and bb. Find a+ba+b.

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