@savvyplayer: Answer 3 and

Answer

3 and -2 🎯

The ordering of the values does not matter to be accepted as the correct answer.

Solution

The problem is very similar to my very first Math challenge problem at https://peakd.com/@savvyplayer/this-is-the-practice-problem/.

When the expression on the original problem is represented in numeric form, we get √(6 + √(6 + √(6 + ...))). Since the expression repeats itself recursively, we can represent the entire expression as x. We now have the equation x = √(6 + x) and should solve for the value of x.

x = √(6 + √(6 + √(6 + ...)))
x = √(6 + x)
x² = 6 + x
x² - x - 6 = 0
(x - 3)(x + 2) = 0
x = 3 or x = -2

Some people might argue that "-2 is not allowed because it will make the radical imaginary". In that case, if you try substituting -2 to the original expression , it will give √(6 + -2) or simply ±2.