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Verified answer
Answer:
3
Step-by-step explanation:
let
y =
[tex] \sqrt{6 + \sqrt{6 + \sqrt{6+ \sqrt{6+ ...} } } } [/tex]
on squaring both side
y^2 =
[tex]6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6...} } } } \\ [/tex]
so
y^2 - y - 6 = 0
y^2 -3y + 2y - 6 = 0
(y - 3)(y +2) = 0
so
y = 3