1/x^6-7/x^3-8=0

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Solution for 1/x^6-7/x^3-8=0 equation: 


D( x )

x^3 = 0

x^6 = 0

x^3 = 0

x^3 = 0

1*x^3 = 0 // : 1

x^3 = 0

x = 0

x^6 = 0

x^6 = 0

1*x^6 = 0 // : 1

x^6 = 0

x = 0

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

1/(x^6)-(7/(x^3))-8 = 0

1/(x^6)-7*x^-3-8 = 0

x^-6-7*x^-3-8 = 0

t_1 = x^-3

1*t_1^2-7*t_1^1-8 = 0

t_1^2-7*t_1-8 = 0

DELTA = (-7)^2-(-8*1*4)

DELTA = 81

DELTA > 0

t_1 = (81^(1/2)+7)/(1*2) or t_1 = (7-81^(1/2))/(1*2)

t_1 = 8 or t_1 = -1

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

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

x in { -1, 1/2 }

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