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 $

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