4x^(-4/5)+8x^(1/5)

Solution for 4x^(-4/5)+8x^(1/5) equation:

D( x )

x = 0

x = 0

x = 0

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

8*x^(1/5)+4*x^(-4/5) = 0

t_1 = x^(1/5)

8*t_1^1+4*t_1^-4 = 0

8*t_1+4*t_1^-4 = 0

4*t_1*(t_1^-5+2) = 0

1*t_1^-5 = -2 // : 1

t_1^-5 = -2

-5 < 0

1/(t_1^5) = -2 // * t_1^5

1 = -2*t_1^5 // : -2

-1/2 = t_1^5

t_1^5 = -1/2 // ^ 1/5

t_1 = -(1/2)^(1/5)

4*t_1 = 0

4*t_1 = 0 // : 4

t_1 = 0

t_1 = -(1/2)^(1/5)

x^(1/5)+(1/2)^(1/5) = 0

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

x^(1/5) = -(1/2)^(1/5)

( -(1/2)^(1/5) < 0 i 1/5 in (0:1) ) => x naleu017Cy do O

t_1 = 0

x^(1/5)+0 = 0

x^(1/5) = 0

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

x^(1/5) = 0

x = 0

x in { 0} 

x belongs to the empty set