# 150 Friends Problem

Algebra Level 5

$\large f(x)= x^{150} + x^{2} -7x + 1$

Let $$x_{1}$$, $$x_{2}$$, $$x_{3}$$$$\ldots$$ $$x_{150}$$ be the roots of the above equation. Define

$\large S = \huge \sum_{i=1}^{150}\dfrac{1}{(1+x_{i})^{2}}$

Find $$|S|$$.

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