x^(1/3)-x^(-2/3)

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Solution for x^(1/3)-x^(-2/3) equation: 


D( x )

x = 0

x = 0

x = 0

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

x^(1/3)-x^(-2/3) = 0

t_1 = x^(1/3)

1*t_1^1-1*t_1^-2 = 0

1*t_1^1-1*t_1^-2 = 0

(1*t_1^3-1*t_1^0)/(t_1^2) = 0 // * t_1^4

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

t_1^2

t_1^3-1 = 0

{ 1, -1 }

1

t_1 = 1

t_1^3-1 = 0

1

t_1-1

t_1^2+t_1+1

t_1^3-1

t_1-1

t_1^2-t_1^3

t_1^2-1

t_1-t_1^2

t_1-1

1-t_1

0

t_1^2+t_1+1 = 0

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

DELTA = -3

DELTA < 0

t_1 in { 1} 

t_1 = 1

x^(1/3)-1 = 0

1*x^(1/3) = 1 // : 1

x^(1/3) = 1

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

x = 1

x = 1

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