X^-2/3+X^-1/3-12=0

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Solution for X^-2/3+X^-1/3-12=0 equation: 


D( X )

X = 0

X = 0

X = 0

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

(X^-1)/3+(X^-2)/3-12 = 0

1/3*X^-1+1/3*X^-2-12 = 0

t_1 = X^-1

1/3*t_1^2+1/3*t_1^1-12 = 0

1/3*t_1^2+1/3*t_1-12 = 0

DELTA = (1/3)^2-(-12*1/3*4)

DELTA = 145/9

DELTA > 0

t_1 = ((145/9)^(1/2)-1/3)/(1/3*2) or t_1 = (-(145/9)^(1/2)-1/3)/(1/3*2)

t_1 = 3/2*((145/9)^(1/2)-1/3) or t_1 = -3/2*((145/9)^(1/2)+1/3)

t_1 = -3/2*((145/9)^(1/2)+1/3)

X^-1-(-3/2*((145/9)^(1/2)+1/3)) = 0

X^-1+3/2*((145/9)^(1/2)+1/3) = 0

1*X^-1 = -(3/2*((145/9)^(1/2)+1/3)) // : 1

X^-1 = -3/2*((145/9)^(1/2)+1/3)

-1 < 0

1/(X^1) = -3/2*((145/9)^(1/2)+1/3) // * X^1

1 = -3/2*((145/9)^(1/2)+1/3)*X^1 // : -3/2*((145/9)^(1/2)+1/3)

-2/3*((145/9)^(1/2)+1/3)^-1 = X^1

X = -2/3*((145/9)^(1/2)+1/3)^-1

t_1 = 3/2*((145/9)^(1/2)-1/3)

X^-1-(3/2*((145/9)^(1/2)-1/3)) = 0

X^-1-3/2*((145/9)^(1/2)-1/3) = 0

1*X^-1 = -(-3/2*((145/9)^(1/2)-1/3)) // : 1

X^-1 = 3/2*((145/9)^(1/2)-1/3)

-1 < 0

1/(X^1) = 3/2*((145/9)^(1/2)-1/3) // * X^1

1 = 3/2*((145/9)^(1/2)-1/3)*X^1 // : 3/2*((145/9)^(1/2)-1/3)

2/3*((145/9)^(1/2)-1/3)^-1 = X^1

X = 2/3*((145/9)^(1/2)-1/3)^-1

X in { -2/3*((145/9)^(1/2)+1/3)^-1, 2/3*((145/9)^(1/2)-1/3)^-1 }

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