Question : $\sqrt{12+\sqrt{12+\sqrt{12+...}}}$ is equal to:
Option 1: 3
Option 2: 4
Option 3: 6
Option 4: 2
Answer (1)
22nd Jan, 2024
Correct Answer: 4
Solution :
Given: Let $x=\sqrt{12+\sqrt{12+\sqrt{12+...}}}$
So, $x=\sqrt{12+x}$
By squaring both sides, we get,
$⇒ x^{2}=(\sqrt{12+x})^{2}$
$ ⇒x^{2}=12+x$
$ ⇒x^{2}-x-12=0$
$⇒x^{2}-4x+3x-12=0$
$⇒ x(x-4) +3(x-4) = 0$
$⇒ (x-4)(x+3) = 0$
$⇒ x = 4$ or $–3$
Hence, the correct answer is 4.
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