x-4/9x^(-1/3)=0

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Solution for x-4/9x^(-1/3)=0 equation:


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

x-((4/9)*x^(-1/3)) = 0

x+(-4/9)*x^(-1/3) = 0

x-4/9*x^(-1/3) = 0

t_1 = x^(1/3)

1*t_1^3-4/9*t_1^-1 = 0

t_1^3-4/9*t_1^-1 = 0

t_1^-1*(t_1^4-4/9) = 0

1*t_1^4 = 4/9 // : 1

t_1^4 = 4/9

t_1^4 = 4/9 // ^ 1/4

abs(t_1) = (4/9)^(1/4)

t_1 = (4/9)^(1/4) or t_1 = -(4/9)^(1/4)

1/t_1 = 0

1*t_1^-1 = 0 // : 1

t_1^-1 = 0

t_1 należy do O

t_1 = (4/9)^(1/4)

x^(1/3)-(4/9)^(1/4) = 0

1*x^(1/3) = (4/9)^(1/4) // : 1

x^(1/3) = (4/9)^(1/4)

x^(1/3) = (4/9)^(1/4) // ^ 3

x = (4/9)^(3/4)

t_1 = -(4/9)^(1/4)

x^(1/3)+(4/9)^(1/4) = 0

1*x^(1/3) = -(4/9)^(1/4) // : 1

x^(1/3) = -(4/9)^(1/4)

( -(4/9)^(1/4) < 0 i 1/3 in (0:1) ) => x należy do O

x = (4/9)^(3/4)

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