An algebra problem by madhav srirangan

Algebra Level 5

Let f ( x ) = x 100 + x 99 + + x + 1 f(x)=x^{100}+x^{99}+\ldots+x+1

x 1 , x 2 , , x 100 x_1,x_2,\ldots,x_{100} are the roots of f ( x ) = 0 f(x)=0 .

Find i = 1 100 1 ( 1 x i ) 2 \displaystyle \sum_{i=1}^{100} \dfrac{1}{(1-x_{i})^{2}} .


The answer is -800.

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1 solution

Can someone please write a solution ? I know no LaTex at all, sorry.

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