Find all real x satisfying this equation:

√(5+√(5-√(5+√(5-√(5+x))))) = x

Prove that there are no others.

I got the same answer as Charlie with Excel; and I note the answer appears to be also expressable as: 1858 ^ (1/8).

If you square both sides, then subtract 5 from both sides,
then square both sides, etc etc you would be left with
(5+x) on the left and a long expression on the right which
you could multiply out. 

I did not go that far but I suspect it would simplify greatly:
I'm guessing to x^8=1858

Posted by Larry on 2012-12-18 01:05:41