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Find the value of 12+12+12+…\sqrt{12 + \sqrt{12 + \sqrt{12 + \dots}}}.

  1. 44

  2. 33

  3. 66

  4. 22

Show answer & explanation

Correct answer

44

Explanation

Let x=12+12+…x = \sqrt{12 + \sqrt{12 + \dots}}. Then x=12+xx = \sqrt{12 + x}. Squaring: x2=12+x⇒x2−x−12=0⇒(x−4)(x+3)=0x^2 = 12 + x \Rightarrow x^2 - x - 12 = 0 \Rightarrow (x-4)(x+3)=0. Since x>0x>0, x=4x=4.

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