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Find \(x = \sqrt{ 3 + \sqrt{ 3 + \sqrt{ 3 + \sqrt{ \ldots } } } } \)

 Jun 30, 2020
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This equals \(x=\sqrt{3+x}\)

Square both sides \(x^2=3+x\).

Then factorize \(x^2-x-3=0\).

Since this expression is clearly positive, x=\(\frac{1+\sqrt{13}}{2}\)

 Jun 30, 2020

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