x^3-64/x^3+64

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Solution for x^3-64/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)

x^3-(64/(x^3))+64 = 0

x^3-64*x^-3+64 = 0

t_1 = x^3

1*t_1^1-64*t_1^-1+64 = 0

1*t_1^1-64*t_1^-1+64*t_1^0 = 0

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

t_1^1*(1*t_1^2+64*t_1^1-64*t_1^0) = 0

t_1^1

t_1^2+64*t_1-64 = 0

t_1^2+64*t_1-64 = 0

DELTA = 64^2-(-64*1*4)

DELTA = 4352

DELTA > 0

t_1 = (4352^(1/2)-64)/(1*2) or t_1 = (-4352^(1/2)-64)/(1*2)

t_1 = (16*17^(1/2)-64)/2 or t_1 = (-16*17^(1/2)-64)/2

t_1 in { (-16*17^(1/2)-64)/2, (16*17^(1/2)-64)/2} 

t_1 = (-16*17^(1/2)-64)/2

x^3-((-16*17^(1/2)-64)/2) = 0

1*x^3 = (-16*17^(1/2)-64)/2 // : 1

x^3 = (-16*17^(1/2)-64)/2

x^3 = (-16*17^(1/2)-64)/2 // ^ 1/3

x = ((-16*17^(1/2)-64)^(1/3))/(2^(1/3))

t_1 = (16*17^(1/2)-64)/2

x^3-((16*17^(1/2)-64)/2) = 0

1*x^3 = (16*17^(1/2)-64)/2 // : 1

x^3 = (16*17^(1/2)-64)/2

x^3 = (16*17^(1/2)-64)/2 // ^ 1/3

x = ((16*17^(1/2)-64)^(1/3))/(2^(1/3))

x in { ((-16*17^(1/2)-64)^(1/3))/(2^(1/3)), ((16*17^(1/2)-64)^(1/3))/(2^(1/3)) }

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