All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution heuristic solution | Comment 1 of 6

By repeatedly replacing the value of x with the formula on the left side, x converges rapidly.  Starting with a guess of x=2, it converges thus:

2.300761708156168
2.302761656377654
2.302775540639462
2.302775637057741
2.302775637727312
2.302775637731962
2.302775637731994
2.302775637731995
2.302775637731995
...

I squared the terminal number to see if this was the square root of an integer or of a rational number, which it was not, but it was exactly 3 higher than the number itself (it came out to 5.302775637731996, the difference in the final digit attributable to rounding differences).

So, solving x^2-3 = x:

x^2 - x - 3 = 0

x = (1 +/- sqrt(1 + 12)) / 2

As the number is positive, we get (1 + sqrt(13)) / 2.

The program:

DEFDBL A-Z
x = 2
FOR i = 1 TO 40
  x = SQR(4 + SQR(4 - SQR(4 + SQR(4 - x))))
  PRINT x
NEXT

 


  Posted by Charlie on 2004-12-24 15:10:29
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information