| \[\sqrt{6+\sqrt{6+\sqrt{6+....}}}\] is equal to |
A) 4
B) 5
C) 3
D) 2
Correct Answer: C
Solution :
| Let \[y=\sqrt{6+y}\] |
| \[\Rightarrow \] \[{{y}^{2}}-y-6=0\] |
| \[\Rightarrow \] \[{{y}^{2}}-3y+2y-6=0\] |
| \[\Rightarrow \] \[y\,(y-3)+2\,(y-3)=0\] |
| \[y=-\,2,\]3 |
| \[y\ne -\,2\] |
| \[\therefore \] \[y=3\] |
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