Question

Value of
\[x =\sqrt{6+\sqrt{6+\sqrt{6+.......\infty}}} \]
is
a.)3
b.)2
c.)1
d.) none of these

Answer 1

x = sqrt(6 + sqrt(6 + sqrt(6 + ...
x^2 = 6 + sqrt(6 + sqrt(6 + ...
x^2 = 6 + x
x^2 - x - 6 = 0
(x-3)(x+2) = 0
x = 3, -2 but -2 is not meaningful here because x > 0
x = 3

Answer 2

vrey nice!