A) 2
B) \[\sqrt{2}\]
C) \[2\sqrt{2}\]
D) \[2+\sqrt{2}\]
Correct Answer: A
Solution :
Let \[x=\sqrt{2+\sqrt{2+...\infty }}\] \[\Rightarrow \] \[{{x}^{2}}=2+x\] \[\Rightarrow \] \[{{x}^{2}}-x-2=0\] \[\Rightarrow \] \[(x+1)(x-2)=0\] \[\Rightarrow \] \[x=2\] \[(\because \,\,x\ne -1)\]You need to login to perform this action.
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