3x=9/x^2

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Solution for 3x=9/x^2 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

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

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

3*x-9*x^-2 = 0

3*x-9*x^-2 = 0

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

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

x^-3 = 1/3

-3 < 0

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

1 = 1/3*x^3 // : 1/3

3 = x^3

x^3 = 3 // ^ 1/3

x = 3^(1/3)

3*x = 0

3*x = 0 // : 3

x = 0

x in { 0} 

x = 3^(1/3)

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