in Quantitative Aptitude edited by
2,119 views
20 votes
20 votes

The value of $\sqrt{12+\sqrt{12+\sqrt{12+\dots}}} $is

  1. $3.464$
  2. $3.932$
  3. $4.000$
  4. $4.444$
in Quantitative Aptitude edited by
2.1k views

2 Answers

23 votes
23 votes
Best answer
$x = \sqrt{12 + x}$

$\implies x^2 = 12 + x$

$\implies x^2 - x - 12 = 0$

$\implies (x-4) (x+3) = 0$

$\implies x = 4 \text{ or } x = -3$

Correct Answer: $C$
edited by
by

2 Comments

X = 4 is taken because sum of positive terms can not be negative.
0
0
As a matter of humor maybe, in just several seconds you can also use GATE calculator for such question.

Just keep calculating till 2-3 times and you'll notice that the pattern is diverging toward one of the answers.

Cheers!
2
2
3 votes
3 votes

there is a really interesting math trick behind it.

If you see a question like this take out the number inside it (in this case is 12)

Take consecutive numbers such as:

$n(n+1)=12$

Always remember that the answer is $n+1$

solve it you get $n=3$ and $n+1=4$

so 4 is the answer.

 

Assume that there is $"-"$ instead of positive then answer would be $n$.

[If we solve by equation then it would be $x^{2}+x-12=0$ giving $x = 3$

 

 

1 comment

Thanks Sir :)
0
0
Answer:

Related questions