Question 81

$$\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + ........}}}} =$$

Solution
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short cut $$2 \times 3 = 6$$

Longer Method

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

$$6 + x = x^2$$

$$x^2 - x - 6 = 0$$

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

$$x = 3, x = -2$$

x = -2 not possible

So answer is x = 3

Hence the answer is option C

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