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} $