Quantitative Aptitude Ques 2116
Question: If $ x=\sqrt{8+\sqrt{8+\sqrt{8…}}} $ and $ y=\sqrt{8-\sqrt{8-\sqrt{8….,}}} $
Options:
A) $ x+y=1 $
B) $ x+y+1=0 $
C) $ x-y=1 $
D) $ x-y+1=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
- $ x=\sqrt{8+\sqrt{8+\sqrt{8+…}}} $ $ x^{2}=8+\sqrt{8\sqrt{8+\sqrt{8+…}}} $
$ \therefore $ $ x^{2}=8+x $ Similarly, $ y^{2}=8-y $
$ \therefore $ $ x^{2}-y^{2}=(x+8)-(8-y) $ $ (x+y)(x-y)=(x+y) $
$ \Rightarrow $ $ x-y=1 $
BETA
