Question

Let $y=\frac{1}{2+\frac{1}{3+\frac{1}{2+\frac{1}{3+.....}}}}$, then $y$ equals.

• A. $\frac{-3\pm \sqrt{15}}{2}$
• B. $\frac{\sqrt{15}-3}{2}$
• C. $\frac{-\sqrt{15}-3}{2}$
• D. None of these

Answer 1

Answer: (A)

$\frac{-3\pm \sqrt{15}}{2}$

$y=\frac{1}{2+\frac{1}{\frac{1}{3+\frac{1}{2+\frac{1}{3+.....}}}}}$

$⟹y=\frac{1}{2+\frac{1}{3+y}}$

$⟹\frac{3+y}{6+2y+1}$

$⟹2y^2+6y-3=0$

$y=\frac{-3\pm \sqrt{15}}{2}$