z^(2/3)-2z^(1/3)-3=0

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Solution for z^(2/3)-2z^(1/3)-3=0 equation: 


z in (-oo:+oo)

z^(2/3)-(2*z^(1/3))-3 = 0

z^(2/3)-2*z^(1/3)-3 = 0

t_1 = z^(1/3)

1*t_1^2-2*t_1^1-3 = 0

t_1^2-2*t_1-3 = 0

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

DELTA = 16

DELTA > 0

t_1 = (16^(1/2)+2)/(1*2) or t_1 = (2-16^(1/2))/(1*2)

t_1 = 3 or t_1 = -1

t_1 = -1

z^(1/3)+1 = 0

1*z^(1/3) = -1 // : 1

z^(1/3) = -1

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

t_1 = 3

z^(1/3)-3 = 0

1*z^(1/3) = 3 // : 1

z^(1/3) = 3

z^(1/3) = 3 // ^ 3

z = 27

z = 27

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