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^-2)/3-((x^-1)/3)-12 = 0

1/3*x^-2-1/3*x^-1-12 = 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 = (1/3-(145/9)^(1/2))/(1/3*2)

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

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

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

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

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

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

-1 < 0

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

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

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

x = 2/3*(1/3-(145/9)^(1/2))^-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*(1/3-(145/9)^(1/2))^-1, 2/3*((145/9)^(1/2)+1/3)^-1 }

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