Question

please answer fast!!!!!!

Answer 1

$Assume\ \sqrt{6 + \sqrt{6 + \sqrt{6 + ......}}} = x \\ \\ \therefore \sqrt{6 + x} = x \\ \\ \\ 6 + x = x^2 \\ \\ x^2 - x = 6 \\ \\ = x(x - 1) = 6 \\ \\ \\ 6 = 3 \times 2 = 3(3 - 1) \\ \\ 6 = (-2) \times (-3) = (-2)(-2 - 1) \\ \\ \\ \therefore x = 3\ OR\ -2$