JEE PYQ: Quadratic Equation Question 3
Question 3 - 2021 (17 Mar Shift 1)
The value of $4 + \dfrac{1}{5 + \dfrac{1}{5 + \dfrac{1}{5 + \cdots}}}$ is:
(1) $2 + \frac{2}{5}\sqrt{30}$
(2) $2 + \frac{4}{5}\sqrt{30}$
(3) $4 + \frac{1}{5}\sqrt{30}$
(4) $5 + \frac{1}{5}\sqrt{30}$
Show Answer
Answer: (1)
Solution
$y = 4 + \dfrac{1}{5 + \frac{1}{5+\frac{1}{\cdots}}}$
$y - 4 = \frac{1}{5 + \frac{1}{(5y+1)}}$
$5y^2 - 20y - 4 = 0$
$y = \frac{20 \pm \sqrt{480}}{10}$
$y = 2 + \sqrt{\frac{480}{100}}$
Correct with Option (A)
BETA
