(27x3-9x2+2)/(3x+1)

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Solution for (27x3-9x2+2)/(3x+1) equation:


D( x )

3*x+1 = 0

3*x+1 = 0

3*x+1 = 0

3*x+1 = 0 // - 1

3*x = -1 // : 3

x = -1/3

x in (-oo:-1/3) U (-1/3:+oo)

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

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

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

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

{ 1, -1, 2, -2 }

1

x = 1

27*x^3-9*x^2+2 = 20

1

-1

x = -1

27*x^3-9*x^2+2 = -34

-1

2

x = 2

27*x^3-9*x^2+2 = 182

2

-2

x = -2

27*x^3-9*x^2+2 = -250

-2

{ 1/3, -1/3, 1/9, -1/9, 1/27, -1/27, -1/3, 1/3, -1/9, 1/9, -1/27, 1/27, 2/3, -2/3, 2/9, -2/9, 2/27, -2/27, -2/3, 2/3, -2/9, 2/9, -2/27, 2/27 }

1/3

x

1/3

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

1/3

-1/3

x

-1/3

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

-1/3

x+1/3

27*x^2-18*x+6

27*x^3-9*x^2+2

x+1/3

-27*x^3-9*x^2

2-18*x^2

18*x^2+6*x

6*x+2

-6*x-2

0

27*x^2-18*x+6 = 0

DELTA = (-18)^2-(4*6*27)

DELTA = -324

DELTA < 0

x in { -1/3}

x+1/3 = 0

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

x+1/3 = 0 // - 1/3

x = -1/3

x in { -1/3}

x belongs to the empty set

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