3x^2-12x/x^3-64

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Solution for 3x^2-12x/x^3-64 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)

3*x^2-((12*x)/(x^3))-64 = 0

3*x^2-12*x^-2-64 = 0

t_1 = x^2

3*t_1^1-12*t_1^-1-64 = 0

3*t_1^1-12*t_1^-1-64*t_1^0 = 0

(3*t_1^2-64*t_1^1-12*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(3*t_1^2-64*t_1^1-12*t_1^0) = 0

t_1^1

3*t_1^2-64*t_1-12 = 0

3*t_1^2-64*t_1-12 = 0

DELTA = (-64)^2-(-12*3*4)

DELTA = 4240

DELTA > 0

t_1 = (4240^(1/2)+64)/(2*3) or t_1 = (64-4240^(1/2))/(2*3)

t_1 = (4*265^(1/2)+64)/6 or t_1 = (64-4*265^(1/2))/6

t_1 in { (64-4*265^(1/2))/6, (4*265^(1/2)+64)/6} 

t_1 = (64-4*265^(1/2))/6

x^2-((64-4*265^(1/2))/6) = 0

1*x^2 = (64-4*265^(1/2))/6 // : 1

x^2 = (64-4*265^(1/2))/6

t_1 = (4*265^(1/2)+64)/6

x^2-((4*265^(1/2)+64)/6) = 0

1*x^2 = (4*265^(1/2)+64)/6 // : 1

x^2 = (4*265^(1/2)+64)/6

x^2 = (4*265^(1/2)+64)/6 // ^ 1/2

abs(x) = ((4*265^(1/2)+64)^(1/2))/(6^(1/2))

x = ((4*265^(1/2)+64)^(1/2))/(6^(1/2)) or x = -(((4*265^(1/2)+64)^(1/2))/(6^(1/2)))

x in { ((4*265^(1/2)+64)^(1/2))/(6^(1/2)), -(((4*265^(1/2)+64)^(1/2))/(6^(1/2))) }

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