TH-TMO 2007 Problem 8

Let $x_1, x_2,... , x_{84}$ be the roots of the equation $x^{84} + 7x - 6 = 0$ . Compute $\sum_{k=1}^{84} \frac{x_k}{x_k-1}$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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