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Four Fours Fancy Formula! (Posted on 2004-12-24) Difficulty: 3 of 5
Find x if √(4+√(4-√(4+√(4-x))))=x.

See The Solution Submitted by Old Original Oskar!    
Rating: 2.2857 (7 votes)

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Some Thoughts re: heuristic solution | Comment 3 of 6 |
(In reply to heuristic solution by Charlie)

The solution found by Charlie (x=½(1+√13)) verifies f(x)=√4+√4-x=x, so the original problem asks for f(f(x))=x. Given this solution, the problem could also have asked for x such that f(f(f(x)))=x, or f(f(f(f(x))))=x, and so on.

A point: if f(x)=x, then obviously f(f(x))=x, but you should prove that no other x such that f(x)≠x can solve the original problem.
  Posted by Federico Kereki on 2004-12-29 13:23:27

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