If x(x\neq0)∊\mathbb{R},then {1}/{1+x+x^{2}}+{1}/{1+x+x^{-1}}+{1}/{1+x^{-1}+x^{2}}=

AP ICET 2016 Paper

Question : 82 of 200

Marks: +1, -0

x(x≠0)∊ℝ,

then

{1}/{1+x+x^{2}}+{1}/{1+x+x^{-1}}+{1}/{1+x^{-1}+x^{2}}=

Solution:

Given : x (≠ 0) ∈ R

{1}/{1+x+x^{2}}+{1}/{1+x+x^{-1}}+{1}/{1+x^{-1}+x^{-2}}

={1}/{1+x+x^{2}}+{x}/{x+x^{2}+1}+{x^{2}}/{x^{2}+x+1}

={1+x+x^{2}}/{1+x+x^{2}}=1

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