The correct option is A 3 Let x=√(6+√(6+√(6+√(6+........... ∞)))) ⇒ x=√(6+x) ⇒ x^2=x+6 ⇒ x^2 x 6=0 ⇒ (x 3)(x+2)=0 ⇒ x=3 # ...

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Algebra of Limits

Evaluate: √...

Question

Evaluate: $\sqrt{6 + \sqrt{6 + \sqrt{6 + . . . . . . . \infty}}}$

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Solution

The correct option is A $3$
Let $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + . . . . . . . . . . . \infty}}}}$

$\Rightarrow x = \sqrt{6 + x}$

$\Rightarrow x^{2} = x + 6$

$\Rightarrow x^{2} - x - 6 = 0$

$\Rightarrow (x - 3) (x + 2) = 0$

$\Rightarrow x = 3$ as it is positive

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