Question

Solve this question immediately
Urgent
Say fast plz

Answer 1

let

$y = \sqrt{20 + \sqrt{20 + \sqrt{20 + ..... \infty } } } \\ squaring \: both \: sides \\ {y}^{2} = 20 + y \\ {y}^{2} - y - 20 = 0 \\ {y}^{2} - 5y + 4y - 20 = 0 \\ y(y - 5) + 4(y - 5) = 0 \\ (y + 4)(y - 5) = 0 \\ y = - 4 \: \: \: or \: \: \: 5 \\ y = - 4 \: (rejected \: becoz \: y \: is \: sq. \: root \: of \: a \: + ve \: no.) \\ therefore \\ \\ \sqrt{20 + \sqrt{20 + \sqrt{20 + ....... \infty } } } = 5$