Quantitative Aptitude Ques 1241

Question: If $ x=\sqrt{12+\sqrt{12+\sqrt{12+\sqrt{12+…}}}} $ and $ y=\sqrt{12-\sqrt{12-\sqrt{12-\sqrt{12-…}}}}, $ then the value of $ x-y $ will be

Options:

A) 0

B) 1

C) 4

D) 2

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ x=\sqrt{12+\sqrt{12+\sqrt{12+}}}…=\sqrt{12+x} $

$ \Rightarrow $ $ \sqrt{12+x}=x $ is satisfied for $ x=4 $ $ y=\sqrt{12-\sqrt{12-\sqrt{12}-}}…=\sqrt{12-y} $

$ \Rightarrow $ $ \sqrt{12-y}=y $ is satisfied for $ y=3 $

$ \therefore $ $ x-y=4-3=1 $

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