Quantitative Aptitude Ques 2458

Question: If $ m=\sqrt{5+\sqrt{5+\sqrt{5+…..}}} $ and $ n=\sqrt{5-\sqrt{5-\sqrt{5-…..}}}, $ then among the following the relation between m and n holds is

Options:

A) $ m+n-1=0 $

B) $ m-n-1=0 $

C)

D)

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ m=\sqrt{5+\sqrt{5+\sqrt{5+….}}} $

$ \Rightarrow $ $ m^{2}=5+m $ [both side squaring]

$ \Rightarrow $ $ m^{2}-m-5=0 $ … (i) $ n=\sqrt{5-\sqrt{5-\sqrt{5-….}}} $

$ \Rightarrow $ $ n^{2}=5-n $ [again, both side squaring]

$ \Rightarrow $ $ n^{2}+n-5=0 $ … (ii) On subtracting Eq. (i) from Eq, (ii), we get $ m^{2}-m-n^{2}-n=0 $

$ \Rightarrow $ $ m^{2}-n^{2}-m-n=0 $

$ \Rightarrow $ $ (m+n)(m-n)-(m+n)=0 $

$ \Rightarrow $ $ (m+n)(m-n-1)=0 $ $ \because $ $ m+n\ne 0 $

$ \therefore $ x

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