6=x+1/x

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Solution for 6=x+1/x equation: 


D( x )

x = 0

x = 0

x = 0

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

6 = x+1/x // - x+1/x

6-x-(1/x) = 0

6-x-x^-1 = 0

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

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

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

x^1

6*x-x^2-1 = 0

6*x-x^2-1 = 0

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

DELTA = 32

DELTA > 0

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

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

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

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

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