A) \[{{6}^{2/3}}\]
B) 6
C) \[3\frac{1}{2}\]
D) 3
Correct Answer: D
Solution :
Let \[x=\sqrt{6+\sqrt{6+\sqrt{6+...}}}\] \[\Rightarrow \] \[x=\sqrt{6+x}\] \[\Rightarrow \] \[{{x}^{2}}=6+x\] \[\Rightarrow \] \[{{x}^{2}}-x-6=0\] \[\Rightarrow \] \[{{x}^{2}}-3x+2x-6=0\] \[\Rightarrow \] \[x\,\,(x+2)+2\,\,(x-3)=0\] \[\Rightarrow \] \[(x+2)(x-3)=0\] \[x=-\,\,2\]and \[x=3\]
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