Quantitative Aptitude Ques 992
Question: $ \sqrt{12+\sqrt{12+\sqrt{12+…}}} $ is equal to
Options:
A) 3
B) 4
C) 6
D) 2
Show Answer
Answer:
Correct Answer: A
Solution:
- Let $ x=\sqrt{12+\sqrt{12+\sqrt{12+…}}} $ On squaring both sides, we get $ x^{2}=12+\sqrt{12+\sqrt{12+…}} $
$ \Rightarrow $ $ x^{2}-12=x $
$ \Rightarrow $ $ x^{2}-x-12=0 $
$ \Rightarrow $ $ x^{2}-4x+3x-12=0 $
$ \Rightarrow $ $ x,(x-4)+3,(x-4)=0 $
$ \Rightarrow $ $ (x+3)(x-4)=0 $
$ \Rightarrow $ $ x=4, $ $ -3 $ Since, x will be positive number.
$ \therefore $ $ x=4, $ $ x\ne 3 $
BETA
