0=3x-x^(1/3)

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


x in (-oo:+oo)

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

x^(1/3)-(3*x)+0 = 0

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

t_1 = x^(1/3)

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

t_1-3*t_1^3 = 0

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

-3*t_1^2 = -1 // : -3

t_1^2 = 1/3

t_1^2 = 1/3 // ^ 1/2

abs(t_1) = (1/3)^(1/2)

t_1 = (1/3)^(1/2) or t_1 = -(1/3)^(1/2)

t_1 = 0

t_1 = 0

t_1 = (1/3)^(1/2)

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

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

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

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

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

t_1 = -(1/3)^(1/2)

x^(1/3)+(1/3)^(1/2) = 0

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

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

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

t_1 = 0

x^(1/3)+0 = 0

x^(1/3) = 0

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

x^(1/3) = 0

x = 0

x in { (1/3)^(3/2), 0 }

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