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Find the value of √(12 + √(12 + √(12 + …))) (continuing without end).

Competition practiceAlgebra

A4
B3
C2√3
D6

Step-by-Step Solution

Call it

y

. Then

y

= √

(12 + y)

, so

y^{2} - y - 12 = 0, (y - 4) (y + 3) = 0

. As

y > 0, y = 4

.

Answer: A) 4

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