Question

find the value
$\sqrt{30 + \sqrt{30 + \sqrt{30... + } } }$

Answer 1

$x = \sqrt{30 + \sqrt{30 + \sqrt{30... + } } } \\ squaring \: both \: side \\ {x}^{2} = 30 + \sqrt{30 + \sqrt{30 + \sqrt{30... + } } } \\ {x}^{2} = 30 + x \\ as \: \sqrt{30 + \sqrt{30 + \sqrt{30... + } } } \: = x \\ {x}^{2} - x - 30 = 0 \\ {x}^{2} - 6x + 5x - 30 = 0 \\ x(x - 6) + 5(x - 6) = 0 \\ (x + 5)(x - 6) = 0 \\ x = - 5 \: \: or \: x = 6 \\ \sqrt{30 + \sqrt{30 + \sqrt{30... + } } } \: \: \: = - 5 \: \: or \: 6$

Answer 2

Hey!

See the attached pic.

Hope it helps u.