Question

$\sqrt{6 + \sqrt{6 + \sqrt{6 + \infty } } }$
Please give the answer fast​

Answer 1

$\huge\mathtt\pink{A}\mathtt\blue{N}\mathtt\purple{S}\mathtt\green{W}\mathtt\orange{E}\mathtt\red{R} \: \: 3$

Step-by-step explanation:

For solving this type of problem let the whole value equal to X and also after one repetition value inside root will become X

$x = \sqrt{6 + x}$

square both side

${x}^{2} = ( { \sqrt{6 + x} })^{2}$

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

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

Hence 2 values of X comes out

$x = 3 \: and \: - 1$

but value under root can only be positive hence

$x = 3$