(1/x^2)-(6/x)+8=0

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Solution for (1/x^2)-(6/x)+8=0 equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

1/(x^2)-(6/x)+8 = 0

1/(x^2)-6*x^-1+8 = 0

x^-2-6*x^-1+8 = 0

t_1 = x^-1

1*t_1^2-6*t_1^1+8 = 0

t_1^2-6*t_1+8 = 0

DELTA = (-6)^2-(1*4*8)

DELTA = 4

DELTA > 0

t_1 = (4^(1/2)+6)/(1*2) or t_1 = (6-4^(1/2))/(1*2)

t_1 = 4 or t_1 = 2

t_1 = 2

x^-1-2 = 0

1*x^-1 = 2 // : 1

x^-1 = 2

-1 < 0

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

1 = 2*x^1 // : 2

1/2 = x^1

x = 1/2

t_1 = 4

x^-1-4 = 0

1*x^-1 = 4 // : 1

x^-1 = 4

-1 < 0

1/(x^1) = 4 // * x^1

1 = 4*x^1 // : 4

1/4 = x^1

x = 1/4

x in { 1/2, 1/4 }

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