Quantitative Aptitude Ques 1264

Question: If $ x+\frac{1}{x}=2, $ then $ x^{2013}+\frac{1}{x^{2014}}=? $

Options:

A) $ 0 $

B) $ 1 $

C) $ -1 $

D) $ 2 $

Show Answer

Answer:

Correct Answer: D

Solution:

  • $ x+\frac{1}{x}=2 $
    $ \Rightarrow $ $ x^{2}-2x+1=0 $

$ \Rightarrow $ $ {{(x-1)}^{2}}=0 $
$ \Rightarrow $ $ x=1 $

$ \therefore $ $ x^{2013}+\frac{1}{x^{2014}}=1+1=2 $

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