Find the positive value of
​$$\sqrt{12 + \sqrt{12 + \sqrt{12 + \sqrt{12 + \dots}}}}$$​​

Correct option is D

Given:

​$$\sqrt{12 + \sqrt{12 + \sqrt{12 + \sqrt{12 + \dots}}}}$$​​

Solution:

$$\sqrt{12 + \sqrt{12 + \sqrt{12 + \sqrt{12 + \dots}}}}$$​ =y

y = 12+y

Squaring on both sides

y²  = 12 + y

y² - y - 12 = 0

y2 - 4y + 3y - 12 = 0

y(y - 4) + 3(y - 4) = 0

(y - 4)(y + 3) = 0

y = 4 or y = -3