# 2017-17 An infimum

For an integer $$n \geq 3$$, evaluate
$\inf \left\{ \sum_{i=1}^n \frac{x_i^2}{(1-x_i)^2} \right\},$
where the infimum is taken over all $$n$$-tuple of real numbers $$x_1, x_2, \dots, x_n \neq 1$$ satisfying that $$x_1 x_2 \dots x_n = 1$$.

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