A) 2
B) 3
C) \[-\,4\]
D) 6
Correct Answer: B
Solution :
Let \[y=\sqrt{6+\sqrt{6+\sqrt{6+...\infty }}}\] \[\Rightarrow \] \[y=\sqrt{6+y}\] \[\Rightarrow \] \[{{y}^{2}}=6+y\] \[\Rightarrow \] \[{{y}^{2}}-y-6=0\] \[\Rightarrow \] \[{{y}^{2}}-3y+2y-6=0\] \[\Rightarrow \] \[(y-3)(y+2)=0\] \[\Rightarrow \] \[y=3\]and \[y\ne -2\] (y cannot be negative) \[\therefore \] Required solution is 3.
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