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

1. $3.464$
2. $3.932$
3. $4.000$
4. $4.444$

$x = \sqrt{12 + x}$

$\implies x^2 = 12 + x$

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

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

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

Correct Answer: $C$
by

X = 4 is taken because sum of positive terms can not be negative.
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!

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 $n+1=4$

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 $x = 3$

Thanks Sir :)

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