Question

the value of
$\sqrt{6 + \sqrt{6 + \sqrt{6 + .....} } }$
(a) 4
(b) - 1/3
(c) 3
(d) 3.5​

Answer 1

Answer:

let

$x = \sqrt{6 + \sqrt{6 + \sqrt{6 + ...} } } \\ x = \sqrt{6 + x } \\ x { }^{2} = 6 + x \\ \\ x ^{2} - x = 6$

therefore by solving the quadratic equation....

x=3,-2

therefore option c is your answer.