Square Root TrickDate: 08/13/97 at 13:09:50 From: Daniel Lee Subject: Square root Is there a formula to calculate sqrt(x+sqrt(x+sqrt(x+... ? Date: 08/18/97 at 14:40:13 From: Doctor Rob Subject: Re: Square root Yes, there is a very cute trick to figure this out. If x = 0, presumably this value is 0. If x < 0, I'm not sure that this makes sense, but perhaps even so. We assume x > 0. Let a = sqrt(x+sqrt(x+sqrt(x+...))). Then square and subtract x. You get a^2 - x = sqrt(x+sqrt(x+...)) = a This is a quadratic equation for a. When you solve it for a, you get two solutions. You must reject one of them as extraneous. That leaves you with the formula you seek. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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