x^(2/3)-8x^(1/3)=9

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Solution for x^(2/3)-8x^(1/3)=9 equation: 


x in (-oo:+oo)

x^(2/3)-(8*x^(1/3)) = 9 // - 9

x^(2/3)-(8*x^(1/3))-9 = 0

x^(2/3)-8*x^(1/3)-9 = 0

t_1 = x^(1/3)

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

t_1^2-8*t_1-9 = 0

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

DELTA = 100

DELTA > 0

t_1 = (100^(1/2)+8)/(1*2) or t_1 = (8-100^(1/2))/(1*2)

t_1 = 9 or t_1 = -1

t_1 = -1

x^(1/3)+1 = 0

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

x^(1/3) = -1

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

t_1 = 9

x^(1/3)-9 = 0

1*x^(1/3) = 9 // : 1

x^(1/3) = 9

x^(1/3) = 9 // ^ 3

x = 729

x = 729

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