How do I solve: (2-sqrt(x)) ^x + (2+sqrt(x)) ^x = 4?

Answer 1

The answer is x = 1.

My answer was verified by using Goal Seek in Excel. I could not get the origional equation to converge using Newton's iterative method so I took the natural log of both sides and then used the Newton's iterative method on this equation to get 1. It was verified using Goal Seek.

If you just stare at the equation, you see that 1 satisfies the equation!