x^(2/3)-8=2x^(1/3)

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Solution for x^(2/3)-8=2x^(1/3) equation: 


x in (-oo:+oo)

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

x^(2/3)-(2*x^(1/3))-8 = 0

x^(2/3)-2*x^(1/3)-8 = 0

t_1 = x^(1/3)

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

t_1^2-2*t_1-8 = 0

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

DELTA = 36

DELTA > 0

t_1 = (36^(1/2)+2)/(1*2) or t_1 = (2-36^(1/2))/(1*2)

t_1 = 4 or t_1 = -2

t_1 = -2

x^(1/3)+2 = 0

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

x^(1/3) = -2

( -2 < 0 i 1/3 in (0:1) ) => x należy do O

t_1 = 4

x^(1/3)-4 = 0

1*x^(1/3) = 4 // : 1

x^(1/3) = 4

x^(1/3) = 4 // ^ 3

x = 64

x = 64

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