(1)/(6x^(2/5))+(1)/(3x^(1/5))-1=0

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Solution for (1)/(6x^(2/5))+(1)/(3x^(1/5))-1=0 equation: 


D( x )

3*x^(1/5) = 0

6*x^(2/5) = 0

3*x^(1/5) = 0

3*x^(1/5) = 0

3*x^(1/5) = 0 // : 3

x^(1/5) = 0

x = 0

6*x^(2/5) = 0

6*x^(2/5) = 0

6*x^(2/5) = 0 // : 6

x^(2/5) = 0

x = 0

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

1/(3*x^(1/5))+1/(6*x^(2/5))-1 = 0

1/3*x^(-1/5)+1/6*x^(-2/5)-1 = 0

t_1 = x^(-1/5)

1/6*t_1^2+1/3*t_1^1-1 = 0

1/6*t_1^2+1/3*t_1-1 = 0

DELTA = (1/3)^2-(-1*1/6*4)

DELTA = 7/9

DELTA > 0

t_1 = ((7/9)^(1/2)-1/3)/(1/6*2) or t_1 = (-(7/9)^(1/2)-1/3)/(1/6*2)

t_1 = 3*((7/9)^(1/2)-1/3) or t_1 = -3*((7/9)^(1/2)+1/3)

t_1 = -3*((7/9)^(1/2)+1/3)

x^(-1/5)-(-3*((7/9)^(1/2)+1/3)) = 0

x^(-1/5)+3*((7/9)^(1/2)+1/3) = 0

1*x^(-1/5) = -(3*((7/9)^(1/2)+1/3)) // : 1

x^(-1/5) = -3*((7/9)^(1/2)+1/3)

-1/5 < 0

1/(x^(1/5)) = -3*((7/9)^(1/2)+1/3) // * x^(1/5)

1 = -3*((7/9)^(1/2)+1/3)*x^(1/5) // : -3*((7/9)^(1/2)+1/3)

1/(-3*((7/9)^(1/2)+1/3)) = x^(1/5)

x^(1/5) = 1/(-3*((7/9)^(1/2)+1/3)) // ^ 5

x = 1/(-243*((7/9)^(1/2)+1/3)^5)

t_1 = 3*((7/9)^(1/2)-1/3)

x^(-1/5)-(3*((7/9)^(1/2)-1/3)) = 0

x^(-1/5)-3*((7/9)^(1/2)-1/3) = 0

1*x^(-1/5) = -(-3*((7/9)^(1/2)-1/3)) // : 1

x^(-1/5) = 3*((7/9)^(1/2)-1/3)

-1/5 < 0

1/(x^(1/5)) = 3*((7/9)^(1/2)-1/3) // * x^(1/5)

1 = 3*((7/9)^(1/2)-1/3)*x^(1/5) // : 3*((7/9)^(1/2)-1/3)

1/(3*((7/9)^(1/2)-1/3)) = x^(1/5)

x^(1/5) = 1/(3*((7/9)^(1/2)-1/3)) // ^ 5

x = 1/(243*((7/9)^(1/2)-1/3)^5)

x in { 1/(-243*((7/9)^(1/2)+1/3)^5), 1/(243*((7/9)^(1/2)-1/3)^5) }

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