x^3-(1/(x^3))=14

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Solution for x^3-(1/(x^3))=14 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-(1/(x^3)) = 14 // - 14

x^3-(1/(x^3))-14 = 0

x^3-x^-3-14 = 0

t_1 = x^3

1*t_1^1-1*t_1^-1-14 = 0

1*t_1^1-1*t_1^-1-14*t_1^0 = 0

(1*t_1^2-14*t_1^1-1*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-14*t_1^1-1*t_1^0) = 0

t_1^1

t_1^2-14*t_1-1 = 0

t_1^2-14*t_1-1 = 0

DELTA = (-14)^2-(-1*1*4)

DELTA = 200

DELTA > 0

t_1 = (200^(1/2)+14)/(1*2) or t_1 = (14-200^(1/2))/(1*2)

t_1 = (10*2^(1/2)+14)/2 or t_1 = (14-10*2^(1/2))/2

t_1 in { (14-10*2^(1/2))/2, (10*2^(1/2)+14)/2} 

t_1 = (14-10*2^(1/2))/2

x^3-((14-10*2^(1/2))/2) = 0

1*x^3 = (14-10*2^(1/2))/2 // : 1

x^3 = (14-10*2^(1/2))/2

x^3 = (14-10*2^(1/2))/2 // ^ 1/3

x = ((14-10*2^(1/2))^(1/3))/(2^(1/3))

t_1 = (10*2^(1/2)+14)/2

x^3-((10*2^(1/2)+14)/2) = 0

1*x^3 = (10*2^(1/2)+14)/2 // : 1

x^3 = (10*2^(1/2)+14)/2

x^3 = (10*2^(1/2)+14)/2 // ^ 1/3

x = ((10*2^(1/2)+14)^(1/3))/(2^(1/3))

x in { ((14-10*2^(1/2))^(1/3))/(2^(1/3)), ((10*2^(1/2)+14)^(1/3))/(2^(1/3)) }

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