MCQ
If $x = \sqrt {1 + \sqrt {1 + \sqrt {1 + .......\infty} } }$, then $x =$
- ✓$\frac{{1 + \sqrt 5 }}{2}$
- B$\frac{{1 - \sqrt 5 }}{2}$
- C$\frac{{1 \pm \sqrt 5 }}{2}$
- DNone of these
We have $x = \sqrt {1 + x} $
==> ${x^2} = 1 + x\,\,\,\, \Rightarrow {x^2} - x - 1 = 0$
==> $x = \frac{{1 \pm \sqrt {1 + 4} }}{2} = \frac{{1 \pm \sqrt 5 }}{2}$
As $x > 0$, we get $x = \frac{{1 + \sqrt 5 }}{2}$
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