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Algebra Level 5

\[\large f(x) = x^{150} + x^{149} + x^{148} + \cdots + x +1\]

Let \(x_{1}\), \(x_{2}\) \(\ldots\) \(x_{150}\) be the roots of the equation \(f(x) = 0\).

Then find the value of

\[\ \sum_{1\leq i < j \leq 150} \dfrac{1}{(1-x_{i})(1-x_{j})}\]


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