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If x+1/x=-1 then x^2016+1/x^2016=?

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If x+1/x=-1 then x^2016+1/x^2016=?
posted May 7, 2017 by anonymous

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1 Answer

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x+1/x = -1
x+1/x+1 =0
(x-1)(x+1/x+1) =0
(x^3)-1 =0
x^3 =1, x≠0

(x^2016)+(1/x^2016) =( x^(3*672))+(1/x^(3*672))
= (1^672) + (1/1^672)
= 1+1 =2.

answer Aug 20, 2017 by anonymous
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