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From: dilvish@dartvax.UUCP (James VanVerth)
Newsgroups: net.puzzle
Subject: Re: x to the x to the x ...
Message-ID: <2966@dartvax.UUCP>
Date: Thu, 25-Apr-85 23:23:17 EDT
Article-I.D.: dartvax.2966
Posted: Thu Apr 25 23:23:17 1985
Date-Received: Sun, 28-Apr-85 06:19:04 EDT
References: <748@whuxlm.UUCP>
Distribution: net
Organization: Dartmouth College, Hanover, NH
Lines: 14

> This one may be old, it's from an old MAA test.
> 
> x^x^x^x... = 2

If you raise x to both sides, you get:
 
x^x^x^x.... = x^2

And by substitution, 2 = x^2, so x = sqrt(2).

Now, how about this one:
 
2 = sqrt(x + sqrt(x + sqrt(x + ... )))