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

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Solution for (9x)-1/(3x^2)=0 equation:


D( x )

3*x^2 = 0

3*x^2 = 0

3*x^2 = 0

3*x^2 = 0 // : 3

x^2 = 0

x = 0

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

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

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

9*x^1-1/3*x^-2 = 0

(9*x^3-1/3*x^0)/(x^2) = 0 // * x^4

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

x^2

9*x^3-1/3 = 0

9*x^3-1/3 = 0 // * 0

{ 1, -1 }

1

x = 1

27*x^3-1 = 26

1

-1

x = -1

27*x^3-1 = -28

-1

{ 1/3, -1/3, 1/9, -1/9, 1/27, -1/27, -1/3, 1/3, -1/9, 1/9, -1/27, 1/27 }

1/3

x

1/3

27*x^3-1 = 0

1/3

x-1/3

27*x^2+9*x+3

27*x^3-1

x-1/3

9*x^2-27*x^3

9*x^2-1

3*x-9*x^2

3*x-1

1-3*x

0

27*x^2+9*x+3 = 0

DELTA = 9^2-(3*4*27)

DELTA = -243

DELTA < 0

x in { 1/3}

x = 1/3

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