Discussion

Explanation:

Suppose, $\sqrt{12+\sqrt{12+\sqrt{12+\dots }}}$  = x

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⇒ $\sqrt{12+x}$ = x

⇒ 12 + x = x²

⇒ x² - x – 12 = 0

⇒ x² – 4x + 3x – 12 = 0

⇒ (x – 4)(x + 3) = 0

⇒ x = 4 or -3.

Since $\sqrt{12+\sqrt{12+\sqrt{12+\dots }}}$  is a positive number, x must also be positive. Hence, only x = 4 will be accepted.

Hence, option (b).

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