Solving Sqrt(x + Sqrt(x + Sqrt(x + ... = 10Date: 02/26/2001 at 00:14:57 From: Anjana Subject: Solving for x in an infinite equation Hi, 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? Thanks. 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 http://mathforum.org/dr.math/ |
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