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

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


x in (-oo:+oo)

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

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

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

t_1 = x^(1/3)

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

t_1^2-8*t_1 = 0

DELTA = (-8)^2-(0*1*4)

DELTA = 64

DELTA > 0

t_1 = (64^(1/2)+8)/(1*2) or t_1 = (8-64^(1/2))/(1*2)

t_1 = 8 or t_1 = 0

t_1 = 0

x^(1/3)+0 = 0

x^(1/3) = 0

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

x^(1/3) = 0

x = 0

t_1 = 8

x^(1/3)-8 = 0

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

x^(1/3) = 8

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

x = 512

x in { 0, 512 }

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