Question

pls solve this... as much fast as you can

Answer 1

$\sqrt{6 + \sqrt{6 + \sqrt{6}..... } } \\ let \: it \: be \: x \\ \sqrt{6 + \sqrt{6 + \sqrt{6.......} } } = x \\ {x}^{2} = 6 + \sqrt{6 + \sqrt{6.....} } \\ now \: we \: have \: considered \: \\ \sqrt{6 + \sqrt{6 + \sqrt{6... = x} } } \\ hence \: {x}^{2} = 6 + x \\ {x}^{2} - x - 6 = 0 \\ {x }^{2} - 3x + 2x - 6 = 0 \\ x(x - 3) + 2(x - 3) = 0 \\ x = - 2 \: or \: x = 3 \\ so \: the \: value \: of \: x \: can \: not \: be \\ negative \: because \: it \: is \: sum \: of \\ \: positive \: roots \: hence \: \\ x = 3$