The value of


The value of $\sqrt{6+\sqrt{6+\sqrt{6+}} \ldots .}$ is

(a) 4
(b) 3
(c) −2
(d) 3.5


Let $x=\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{6+} \ldots . .}}}$

Squaring both sides we get

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



$x^{2}-3 x+2 x-6=0$




The value of x cannot be negative.

Thus, the value of x = 3

Therefore, the correct answer is $(b)$

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