SOLUTION: Evaluate sqrt[12+sqrt(12+sqrt(12+...]

Question 1199930: Evaluate sqrt[12+sqrt(12+sqrt(12+...]

Found 2 solutions by TonyChopper, ikleyn:
Answer by TonyChopper(3)   (Show Source): You can put this solution on YOUR website!
sqrt[12+sqrt(12+sqrt(12+...] can be shown as x = sqrt(12+x)
When both sides are squared, the equation becomes x^2 = 12 + x
x^2 = 12 + x
0 = x^2 + x + 12
0 = (x+3)(x-4)
In order for the equation to hold true, x must either be -3, or 4
If we substitute -3 and 4 into x = sqrt(12+x), we find that -3 does not satisfy our equation while 4 does.
Therefore sqrt[12+sqrt(12+sqrt(12+...] is equal to 4

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

If you want to see many other similar problems solved and explained, look into the lesson
    - Evaluating expressions that contain infinitely many square roots
in this site.

The current problem is also solved there (Problem 4).

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