Question

√{2+√(2+√2+........)}=?​

Answer 1

Answer:

$let \: \sqrt{2 + \sqrt{2 + \sqrt{2 + .....} } } \: \: be \: x$

$\sqrt{2 + x} = \: x \\ squaring \: both \: sides$

2 + x = x²

x² - x - 2 = 0

x² - 2x + 1x - 2 = 0

x(x - 2) + 1(x - 2)

(x - 2)(x + 1) = 0

either (x-2) can be zero or (x+1) can be zero

x = 2, -1

-1 value of x will be rejected

so,

x = 2