x^(4/3)-9x^(2/3)+8=0

Solution for x^(4/3)-9x^(2/3)+8=0 equation:

x in (-oo:+oo)

x^(4/3)-(9*x^(2/3))+8 = 0

x^(4/3)-9*x^(2/3)+8 = 0

t_1 = x^(2/3)

1*t_1^2-9*t_1^1+8 = 0

t_1^2-9*t_1+8 = 0

DELTA = (-9)^2-(1*4*8)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+9)/(1*2) or t_1 = (9-49^(1/2))/(1*2)

t_1 = 8 or t_1 = 1

t_1 = 1

x^(2/3)-1 = 0

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

x^(2/3) = 1

x^(2/3) = 1 // ^ 3

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

t_1 = 8

x^(2/3)-8 = 0

1*x^(2/3) = 8 // : 1

x^(2/3) = 8

x^(2/3) = 8 // ^ 3

x^2 = 512 // ^ 1/2

abs(x) = 16*2^(1/2)

x = 16*2^(1/2) or x = -(16*2^(1/2))

x in { 1, -1, 16*2^(1/2), -(16*2^(1/2)) }