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MATH / Let x₁, x₂, …, x₂₀₁₆ be the roots of

Problem

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problem

Let x1,x_1, x2,x_2, …,\dots, x2016x_{2016} be the roots of x2016+x2015+…+x+1=0.x^{2016} + x^{2015} + \dots + x + 1 = 0.Find 1(1−x1)2+1(1−x2)2+…+1(1−x2016)2.\frac{1}{(1 - x_1)^2} + \frac{1}{(1 - x_2)^2} + \dots + \frac{1}{(1 - x_{2016})^2}.
Plain-text mathematical notation (without MathML)
Let x₁, x₂, …, x₂₀₁₆ be the roots of
x²⁰¹⁶+x²⁰¹⁵+…+x+1=0.Find
(1)/((1−x₁)²)+(1)/((1−x₂)²)+…+(1)/((1−x₂₀₁₆)²).
Original LaTeX notation
Let $x_1,$ $x_2,$ $\dots,$ $x_{2016}$ be the roots of
\[x^{2016} + x^{2015} + \dots + x + 1 = 0.\]Find
\[\frac{1}{(1 - x_1)^2} + \frac{1}{(1 - x_2)^2} + \dots + \frac{1}{(1 - x_{2016})^2}.\]

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
8a102f62-5ddf-59f4-b405-83af1240d732
task_key
intermediate~5falgebra--test--8a102f62-5ddf-59f4-b405-83af1240d732
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import