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Solving Sqrt(x + Sqrt(x + Sqrt(x + ... = 10

Date: 02/26/2001 at 00:14:57
From: Anjana
Subject: Solving for x in an infinite equation


I would like to know how it is possible to solve the following 
infinite equation for x, if x is known to be a real number:

     sqrt(x + sqrt(x + sqrt(x + sqrt(x + ... = 10

I'm not sure where to start, much less how to solve for x. Squaring 
the left side of the equation repeatedly (which you couldn't do 
indefinitely), it seems to get more and more complicated. Any ideas?


Date: 02/26/2001 at 10:01:02
From: Doctor Rob
Subject: Re: Solving for x in an infinite equation

Thanks for writing to Ask Dr. Math, Anjana.

Square both sides, then subtract x from both sides. Then the left-hand 
side of the equation is just, from the starting equation, 10.

Now solve the resulting equation for x.

- Doctor Rob, The Math Forum   
Associated Topics:
High School Basic Algebra

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