A) 1.42
B) 4
C) 2
D) 2.414
Correct Answer: C
Solution :
Let \[=\sqrt{2+\sqrt{2+\sqrt{2+.....}}}\] \[={{x}^{2}}=2+\sqrt{2+\sqrt{2+\sqrt{2+.....}}}\] \[={{x}^{2}}=2+x\] \[={{x}^{2}}-x-2=0\] \[={{x}^{2}}-2x+x-2=0\] \[x(x-2)+1(x-2)=0\] \[\Rightarrow \] \[(x-2)(x+1)=0\] \[\Rightarrow \] \[x=2,\] because the numbers are positiveYou need to login to perform this action.
You will be redirected in
3 sec