3x^(-1/3)-x^(-1/6)-10=0

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Solution for 3x^(-1/3)-x^(-1/6)-10=0 equation: 


D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

3*x^(-1/3)-x^(-1/6)-10 = 0

t_1 = x^(-1/6)

3*t_1^2-1*t_1^1-10 = 0

3*t_1^2-t_1-10 = 0

DELTA = (-1)^2-(-10*3*4)

DELTA = 121

DELTA > 0

t_1 = (121^(1/2)+1)/(2*3) or t_1 = (1-121^(1/2))/(2*3)

t_1 = 2 or t_1 = -5/3

t_1 = -5/3

x^(-1/6)+5/3 = 0

1*x^(-1/6) = -5/3 // : 1

x^(-1/6) = -5/3

-1/6 < 0

1/(x^(1/6)) = -5/3 // * x^(1/6)

1 = -5/3*x^(1/6) // : -5/3

-3/5 = x^(1/6)

x^(1/6) = -3/5 // ^ 6

x = 729/15625

t_1 = 2

x^(-1/6)-2 = 0

1*x^(-1/6) = 2 // : 1

x^(-1/6) = 2

-1/6 < 0

1/(x^(1/6)) = 2 // * x^(1/6)

1 = 2*x^(1/6) // : 2

1/2 = x^(1/6)

x^(1/6) = 1/2 // ^ 6

x = 1/64

x in { 729/15625, 1/64 }

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