x^-2/3+3x^-1/3=28

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Solution for x^-2/3+3x^-1/3=28 equation: 


D( x )

x = 0

x = 0

x = 0

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

(3*x^-1)/3+(x^-2)/3 = 28 // - 28

(3*x^-1)/3+(x^-2)/3-28 = 0

x^-1+1/3*x^-2-28 = 0

t_1 = x^-1

1/3*t_1^2+1*t_1^1-28 = 0

1/3*t_1^2+t_1-28 = 0

DELTA = 1^2-(-28*1/3*4)

DELTA = 115/3

DELTA > 0

t_1 = ((115/3)^(1/2)-1)/(1/3*2) or t_1 = (-(115/3)^(1/2)-1)/(1/3*2)

t_1 = 3/2*((115/3)^(1/2)-1) or t_1 = -3/2*((115/3)^(1/2)+1)

t_1 = -3/2*((115/3)^(1/2)+1)

x^-1-(-3/2*((115/3)^(1/2)+1)) = 0

x^-1+3/2*((115/3)^(1/2)+1) = 0

1*x^-1 = -(3/2*((115/3)^(1/2)+1)) // : 1

x^-1 = -3/2*((115/3)^(1/2)+1)

-1 < 0

1/(x^1) = -3/2*((115/3)^(1/2)+1) // * x^1

1 = -3/2*((115/3)^(1/2)+1)*x^1 // : -3/2*((115/3)^(1/2)+1)

-2/3*((115/3)^(1/2)+1)^-1 = x^1

x = -2/3*((115/3)^(1/2)+1)^-1

t_1 = 3/2*((115/3)^(1/2)-1)

x^-1-(3/2*((115/3)^(1/2)-1)) = 0

x^-1-3/2*((115/3)^(1/2)-1) = 0

1*x^-1 = -(-3/2*((115/3)^(1/2)-1)) // : 1

x^-1 = 3/2*((115/3)^(1/2)-1)

-1 < 0

1/(x^1) = 3/2*((115/3)^(1/2)-1) // * x^1

1 = 3/2*((115/3)^(1/2)-1)*x^1 // : 3/2*((115/3)^(1/2)-1)

2/3*((115/3)^(1/2)-1)^-1 = x^1

x = 2/3*((115/3)^(1/2)-1)^-1

x in { -2/3*((115/3)^(1/2)+1)^-1, 2/3*((115/3)^(1/2)-1)^-1 }

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