2x-1/x=5

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Solution for 2x-1/x=5 equation: 


D( x )

x = 0

x = 0

x = 0

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

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

2*x-(1/x)-5 = 0

2*x-x^-1-5 = 0

2*x^1-1*x^-1-5*x^0 = 0

(2*x^2-5*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(2*x^2-5*x^1-1*x^0) = 0

x^1

2*x^2-5*x-1 = 0

2*x^2-5*x-1 = 0

DELTA = (-5)^2-(-1*2*4)

DELTA = 33

DELTA > 0

x = (33^(1/2)+5)/(2*2) or x = (5-33^(1/2))/(2*2)

x = (33^(1/2)+5)/4 or x = (5-33^(1/2))/4

x in { (5-33^(1/2))/4, (33^(1/2)+5)/4} 

x in { (5-33^(1/2))/4, (33^(1/2)+5)/4 }

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