A) \[\frac{1+\sqrt{5}}{2}\]
B) \[\frac{1-\sqrt{5}}{2}\]
C) \[\frac{1\pm \sqrt{5}}{2}\]
D) None of these
Correct Answer: A
Solution :
\[x=\sqrt{1+\sqrt{1+\sqrt{1+.....}}}\]to \[\infty \]\[\infty \] We have \[x=\sqrt{1+x}\] Þ \[{{x}^{2}}=1+x\,\,\,\,\Rightarrow {{x}^{2}}-x-1=0\] Þ \[x=\frac{1\pm \sqrt{1+4}}{2}=\frac{1\pm \sqrt{5}}{2}\] As\[x>0\], we get \[x=\frac{1+\sqrt{5}}{2}\]You need to login to perform this action.
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