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
BETA
