Quantitative Aptitude Ques 2096
Question: If $ x-\frac{1}{x}=4, $ then $ ( x+\frac{1}{x} ) $ is equal to
Options:
A) $ 5\sqrt{2} $
B) $ 2\sqrt{5} $
C) (c) $ 4\sqrt{2} $
D) $ 4\sqrt{5} $
Show Answer
Answer:
Correct Answer: B
Solution:
- $ x-\frac{1}{x}=4 $ [given] On squaring both sides, we get $ {{( x-\frac{1}{x} )}^{2}}=4^{2} $
$ \Rightarrow $ $ x^{2}+\frac{1}{x^{2}}-2\times x\times \frac{1}{x}=16 $
$ \Rightarrow $ $ x^{2}+\frac{1}{x^{2}}=16+2=18 $ On adding 2 both sides, we get $ x^{2}+\frac{1}{x^{2}}+2=18+2 $
$ \Rightarrow $ $ {{( x+\frac{1}{x} )}^{2}}=20 $
$ \therefore $ $ x+\frac{1}{x}=\sqrt{20}=2\sqrt{5} $
BETA
