A) \[\frac{1\pm \sqrt{13}}{2}\]
B) \[\frac{1\pm \sqrt{3i}}{2}\]
C) \[\frac{1\pm \sqrt{6}}{2}\]
D) \[\frac{1\pm \sqrt{3}}{2}\]
Correct Answer: A
Solution :
(a): Let \[y=\sqrt{3+\sqrt{3+\sqrt{3+........}}}\] \[\Rightarrow y=\sqrt{3+y}\] \[\Rightarrow {{y}^{2}}=3+y\] \[\Rightarrow {{y}^{2}}-y-3=0\] \[\Rightarrow y=\frac{1\pm \sqrt{13}}{2}\]
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