x=(1/x)-1

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Solution for x=(1/x)-1 equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

x = 1/x-1 // - 1/x-1

x-(1/x)+1 = 0

x-x^-1+1 = 0

1*x^1-1*x^-1+1*x^0 = 0

(1*x^2+1*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2+1*x^1-1*x^0) = 0

x^1

x^2+x-1 = 0

x^2+x-1 = 0

DELTA = 1^2-(-1*1*4)

DELTA = 5

DELTA > 0

x = (5^(1/2)-1)/(1*2) or x = (-5^(1/2)-1)/(1*2)

x = (5^(1/2)-1)/2 or x = (-(5^(1/2)+1))/2

x in { (-(5^(1/2)+1))/2, (5^(1/2)-1)/2} 

x in { (-(5^(1/2)+1))/2, (5^(1/2)-1)/2 }

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