2x-1=1/x

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Solution for 2x-1=1/x equation: 


D( x )

x = 0

x = 0

x = 0

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

2*x-1 = 1/x // - 1/x

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

2*x-x^-1-1 = 0

2*x^1-1*x^-1-1*x^0 = 0

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

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

x^1

2*x^2-x-1 = 0

2*x^2-x-1 = 0

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

DELTA = 9

DELTA > 0

x = (9^(1/2)+1)/(2*2) or x = (1-9^(1/2))/(2*2)

x = 1 or x = -1/2

x in { -1/2, 1} 

x in { -1/2, 1 }

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