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MathNet 2008-part-02 — 165 problems (EN–VI) Question 69

Math Olympiad Vault · MathNet 2008-part-02 — 165 problems (EN–VI)

Question 69

Denoting by $x_{1}, x_{2}, x_{3}$ and $x_{4}$ the solutions of the equation $x^{4}-2 x^{3}-7 x^{2}-2 x+1=0$, what is the value of $\frac{1}{x_{1}}+\frac{1}{x_{2}}+\frac{1}{x_{3}}+\frac{1}{x_{4}}$?

(A) 1
(B) $\frac{1}{2}$
(C) 2
(D) 4
(E) 7.