HMMT 2008 E7

The equation $x^{3}-9 x^{2}+8 x+2=0$ has three real roots $p, q, r$ . Find $\frac{1}{p^{2}}+\frac{1}{q^{2}}+\frac{1}{r^{2}}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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