8x^3/2-8x^-3/2-63=0

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Solution for 8x^3/2-8x^-3/2-63=0 equation: 


D( x )

x = 0

x = 0

x = 0

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

(8*x^3)/2-((8*x^-3)/2)-63 = 0

(8*x^3)/2-4*x^-3-63 = 0

4*x^3-4*x^-3-63 = 0

t_1 = x^3

4*t_1^1-4*t_1^-1-63 = 0

4*t_1^1-4*t_1^-1-63*t_1^0 = 0

(4*t_1^2-63*t_1^1-4*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(4*t_1^2-63*t_1^1-4*t_1^0) = 0

t_1^1

4*t_1^2-63*t_1-4 = 0

4*t_1^2-63*t_1-4 = 0

DELTA = (-63)^2-(-4*4*4)

DELTA = 4033

DELTA > 0

t_1 = (4033^(1/2)+63)/(2*4) or t_1 = (63-4033^(1/2))/(2*4)

t_1 = (4033^(1/2)+63)/8 or t_1 = (63-4033^(1/2))/8

t_1 in { (63-4033^(1/2))/8, (4033^(1/2)+63)/8} 

t_1 = (63-4033^(1/2))/8

x^3-((63-4033^(1/2))/8) = 0

1*x^3 = (63-4033^(1/2))/8 // : 1

x^3 = (63-4033^(1/2))/8

x^3 = (63-4033^(1/2))/8 // ^ 1/3

x = ((63-4033^(1/2))^(1/3))/2

t_1 = (4033^(1/2)+63)/8

x^3-((4033^(1/2)+63)/8) = 0

1*x^3 = (4033^(1/2)+63)/8 // : 1

x^3 = (4033^(1/2)+63)/8

x^3 = (4033^(1/2)+63)/8 // ^ 1/3

x = ((4033^(1/2)+63)^(1/3))/2

x in { ((63-4033^(1/2))^(1/3))/2, ((4033^(1/2)+63)^(1/3))/2 }

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