x^(-2/3)+x^(-1/3)-72=0

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Solution for x^(-2/3)+x^(-1/3)-72=0 equation: 


D( x )

x = 0

x = 0

x = 0

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

x^(-1/3)+x^(-2/3)-72 = 0

t_1 = x^(-1/3)

1*t_1^2+1*t_1^1-72 = 0

t_1^2+t_1-72 = 0

DELTA = 1^2-(-72*1*4)

DELTA = 289

DELTA > 0

t_1 = (289^(1/2)-1)/(1*2) or t_1 = (-289^(1/2)-1)/(1*2)

t_1 = 8 or t_1 = -9

t_1 = -9

x^(-1/3)+9 = 0

1*x^(-1/3) = -9 // : 1

x^(-1/3) = -9

-1/3 < 0

1/(x^(1/3)) = -9 // * x^(1/3)

1 = -9*x^(1/3) // : -9

-1/9 = x^(1/3)

x^(1/3) = -1/9 // ^ 3

x = -1/729

t_1 = 8

x^(-1/3)-8 = 0

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

x^(-1/3) = 8

-1/3 < 0

1/(x^(1/3)) = 8 // * x^(1/3)

1 = 8*x^(1/3) // : 8

1/8 = x^(1/3)

x^(1/3) = 1/8 // ^ 3

x = 1/512

x in { -1/729, 1/512 }

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