Quantitative Aptitude Ques 169

Question: The mean of x and 1/x is N. Then, the mean of $ x^{2} $ and $ 1/x^{2} $ is

Options:

A) $ N^{2}-2 $

B) $ 2,N^{2}-2 $

C) $ 4,N^{2}-2 $

D) $ N^{2} $

Show Answer

Answer:

Correct Answer: B

Solution:

  • According to the question, $ \frac{1}{2}( x+\frac{1}{x} )=N $
    $ \Rightarrow $ $ ( x+\frac{1}{x} )=2N $

$ \Rightarrow $ $ x^{2}+\frac{1}{x^{2}}+2=4N^{2} $ [squaring both sides]

$ \Rightarrow $ $ x^{2}+\frac{1}{x^{2}}=4N^{2}-2=2,(2N^{2}-1) $

$ \Rightarrow $ $ \frac{1}{2}( x^{2}+\frac{1}{x^{2}} )=(2N^{2}-1) $ [divide both sides by 2] Hence, mean of $ x^{2} $ and $ \frac{1}{x^{2}} $ is $ (2N^{2}-1). $

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