(1/x^3)^2+9(1/x^3)+8=0

Solution for (1/x^3)^2+9(1/x^3)+8=0 equation:

D( x )

x^3 = 0

x^3 = 0

x^3 = 0

1*x^3 = 0 // : 1

x^3 = 0

x = 0

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

9*(1/(x^3))+(1/(x^3))^2+8 = 0

9*x^-3+x^-6+8 = 0

t_1 = x^-3

1*t_1^2+9*t_1^1+8 = 0

t_1^2+9*t_1+8 = 0

DELTA = 9^2-(1*4*8)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)-9)/(1*2) or t_1 = (-49^(1/2)-9)/(1*2)

t_1 = -1 or t_1 = -8

t_1 = -8

x^-3+8 = 0

1*x^-3 = -8 // : 1

x^-3 = -8

-3 < 0

1/(x^3) = -8 // * x^3

1 = -8*x^3 // : -8

-1/8 = x^3

x^3 = -1/8 // ^ 1/3

x = -1/2

t_1 = -1

x^-3+1 = 0

1*x^-3 = -1 // : 1

x^-3 = -1

-3 < 0

1/(x^3) = -1 // * x^3

1 = -1*x^3 // : -1

-1 = x^3

x^3 = -1 // ^ 1/3

x = -1

x in { -1/2, -1 }