125x^(1/3)-25x^(-2/3)

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Solution for 125x^(1/3)-25x^(-2/3) equation:


D( x )

x = 0

x = 0

x = 0

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

125*x^(1/3)-(25*x^(-2/3)) = 0

125*x^(1/3)-25*x^(-2/3) = 0

t_1 = x^(1/3)

125*t_1^1-25*t_1^-2 = 0

125*t_1-25*t_1^-2 = 0

25*t_1*(5-t_1^-3) = 0

-1*t_1^-3 = -5 // : -1

t_1^-3 = 5

-3 < 0

1/(t_1^3) = 5 // * t_1^3

1 = 5*t_1^3 // : 5

1/5 = t_1^3

t_1^3 = 1/5 // ^ 1/3

t_1 = (1/5)^(1/3)

25*t_1 = 0

25*t_1 = 0 // : 25

t_1 = 0

t_1 = (1/5)^(1/3)

x^(1/3)-(1/5)^(1/3) = 0

1*x^(1/3) = (1/5)^(1/3) // : 1

x^(1/3) = (1/5)^(1/3)

x^(1/3) = (1/5)^(1/3) // ^ 3

x = 1/5

t_1 = 0

x^(1/3)+0 = 0

x^(1/3) = 0

1*x^(1/3) = 0 // : 1

x^(1/3) = 0

x = 0

x in { 0}

x = 1/5

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