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Question : $\sqrt{12+\sqrt{12+\sqrt{12+...}}}$ is equal to:

Option 1: 3

Option 2: 4

Option 3: 6

Option 4: 2


Team Careers360 21st Jan, 2024
Answer (1)
Team Careers360 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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