Question

If x = $\sqrt{1 + \sqrt{1 + \sqrt{1 + .........\infty}}}$ then x is equal to :

• A. $\frac{1 + \sqrt{5}}{2}$
• B. $\frac{1–\sqrt{5}}{2}$
• C. $\frac{1 \pm \sqrt{5}}{2}$
• D. None of these

Answer 1

Answer: (A)

$\frac{1 + \sqrt{5}}{2}$

Answer 2

Let x=$\sqrt{1 + x}$or x² = 1 + x; i.e., x²–x– 1= 0

x =1±$\sqrt{5}$/2 so x = 1+$\sqrt{5}$/2 (As x ¹ 1–$\sqrt{5}$/2)