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Given $3n$ positive numbers $a_1, \ldots, a_n$, $b_1, \ldots, b_n$, and $x_1, \ldots, x_n$, we are given a function $$f(x) = \sum_{i = 1}^n \frac{a_i}{\sqrt{(x - x_i)^2 + b_i}}.$$ Can we find all the ...