x=5/2-1/x

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


D( x )

x = 0

x = 0

x = 0

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

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

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

x+1/x-5/2 = 0

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

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

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

x^1

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

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

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

DELTA = 9/4

DELTA > 0

x = ((9/4)^(1/2)-(-5/2))/(1*2) or x = (-(-5/2)-(9/4)^(1/2))/(1*2)

x = 2 or x = 1/2

x in { 1/2, 2} 

x in { 1/2, 2 }

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