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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