Solution
Let $$\sqrt{6+\sqrt{6+\sqrt{6+.....\ }}}\ =\ x$$ ..........(1)
$$\sqrt{6+(\sqrt{6+\sqrt{6+.....\ }})}=x$$.........(2)
Substitute equation (1) in (2)
$$\sqrt{6+(x)}\ =\ x$$ (or) $$x^{2} - x - 6 = 0$$
$$x = 3, -2$$. But '$$x$$' value should be positive
$$\therefore x = 3$$
Hence, option D is the correct answer.
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