460 views

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

1. $3.464$
2. $3.932$
3. $4.000$
4. $4.444$
edited | 460 views

$x = \sqrt{12 + x}$

$\implies x^2 = 12 + x$

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

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

$\implies x = 4 \text{ or } x = -3$
0
X = 4 is taken because sum of positive terms can not be negative.
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!
c) 4.000