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MathNet 2008-part-05 — 164 problems (EN–VI) Question 103

Math Olympiad Vault · MathNet 2008-part-05 — 164 problems (EN–VI)

Question 103

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