Question : $\sqrt{12+\sqrt{12+\sqrt{12+...}}}$ is equal to:
Option 1: 3
Option 2: 4
Option 3: 6
Option 4: 2
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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