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

1/3*x^-1+1/3*x^-2-72 = 0

t_1 = x^-1

1/3*t_1^2+1/3*t_1^1-72 = 0

1/3*t_1^2+1/3*t_1-72 = 0

DELTA = (1/3)^2-(-72*1/3*4)

DELTA = 865/9

DELTA > 0

t_1 = ((865/9)^(1/2)-1/3)/(1/3*2) or t_1 = (-(865/9)^(1/2)-1/3)/(1/3*2)

t_1 = 3/2*((865/9)^(1/2)-1/3) or t_1 = -3/2*((865/9)^(1/2)+1/3)

t_1 = -3/2*((865/9)^(1/2)+1/3)

x^-1-(-3/2*((865/9)^(1/2)+1/3)) = 0

x^-1+3/2*((865/9)^(1/2)+1/3) = 0

1*x^-1 = -(3/2*((865/9)^(1/2)+1/3)) // : 1

x^-1 = -3/2*((865/9)^(1/2)+1/3)

-1 < 0

1/(x^1) = -3/2*((865/9)^(1/2)+1/3) // * x^1

1 = -3/2*((865/9)^(1/2)+1/3)*x^1 // : -3/2*((865/9)^(1/2)+1/3)

-2/3*((865/9)^(1/2)+1/3)^-1 = x^1

x = -2/3*((865/9)^(1/2)+1/3)^-1

t_1 = 3/2*((865/9)^(1/2)-1/3)

x^-1-(3/2*((865/9)^(1/2)-1/3)) = 0

x^-1-3/2*((865/9)^(1/2)-1/3) = 0

1*x^-1 = -(-3/2*((865/9)^(1/2)-1/3)) // : 1

x^-1 = 3/2*((865/9)^(1/2)-1/3)

-1 < 0

1/(x^1) = 3/2*((865/9)^(1/2)-1/3) // * x^1

1 = 3/2*((865/9)^(1/2)-1/3)*x^1 // : 3/2*((865/9)^(1/2)-1/3)

2/3*((865/9)^(1/2)-1/3)^-1 = x^1

x = 2/3*((865/9)^(1/2)-1/3)^-1

x in { -2/3*((865/9)^(1/2)+1/3)^-1, 2/3*((865/9)^(1/2)-1/3)^-1 }

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