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If x = 1 + x/(2 + x/(2 + x/(2 + x/(2 + ...)))), then what is x?

 May 28, 2021
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x = 1 + x/(2 + x/(2 + x/(2 + x/(2 + ...))))

x - 1 = x/(2 + x - 1)

x - 1 = x/(x+1)

x^2 - 1 = x

x^2 - x - 1 = 0

 

Solve for x :))

 

=^._.^=

 May 28, 2021

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