Question

if x=√6+√6+√6........ then x=

Answer 1

$given \: \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + .........} } } } } = x \\ = > \: \sqrt{6 + x } = x \\ = > 6 + x = {x}^{2} \\ = > {x}^{2} - x - 6 = 0 \\ = > {x}^{2} - 3x + 2x - 6 = 0 \\ = > x(x - 3) + 2(x - 3) = 0 \\ = > (x - 3)(x + 2) = 0 \\ = > x = 3 \: (or) \: x = - 2$