x+1/x=6

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Solution for x+1/x=6 equation: 


D( x )

x = 0

x = 0

x = 0

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

x+1/x = 6 // - 6

x+1/x-6 = 0

1*x^1+1*x^-1-6*x^0 = 0

(1*x^2-6*x^1+1*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-6*x^1+1*x^0) = 0

x^1

x^2-6*x+1 = 0

x^2-6*x+1 = 0

DELTA = (-6)^2-(1*1*4)

DELTA = 32

DELTA > 0

x = (32^(1/2)+6)/(1*2) or x = (6-32^(1/2))/(1*2)

x = (4*2^(1/2)+6)/2 or x = (6-4*2^(1/2))/2

x in { (6-4*2^(1/2))/2, (4*2^(1/2)+6)/2} 

x in { (6-4*2^(1/2))/2, (4*2^(1/2)+6)/2 }

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