150 Friends Problem

Algebra Level 5

f(x)=x150+x27x+1\large f(x)= x^{150} + x^{2} -7x + 1

Let x1x_{1}, x2x_{2}, x3x_{3}\ldots x150x_{150} be the roots of the above equation. Define

S=i=11501(1+xi)2\large S = \huge \sum_{i=1}^{150}\dfrac{1}{(1+x_{i})^{2}}

Find S |S| .

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