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). $
BETA
