Question

$\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + \infty } } } }$


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Answer 1

Let,

$\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + \infty } } } } = y \\ \\ = > \sqrt{6 + y} = y \\ \\ = > 6 + y = {y}^{2} \\ \\ = > {y}^{2} - y - 6 = 0 \\ \\ = > {y}^{2} - 3y + 2y - 6 = 0 \\ \\ = > y(y - 3) + 2(y - 3) = 0 \\ \\ = > (y - 3)( y+ 2) = 0$

Required values of y : 3 and -2

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