x-1/x^2+5x+11

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Solution for x-1/x^2+5x+11 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)

x+5*x-(1/(x^2))+11 = 0

x+5*x-x^-2+11 = 0

6*x^1-1*x^-2+11*x^0 = 0

(6*x^3+11*x^2-1*x^0)/(x^2) = 0 // * x^4

x^2*(6*x^3+11*x^2-1*x^0) = 0

x^2

6*x^3+11*x^2-1 = 0

{ 1, -1 }

1

x = 1

6*x^3+11*x^2-1 = 16

1

-1

x = -1

6*x^3+11*x^2-1 = 4

-1

{ 1/2, -1/2, 1/3, -1/3, 1/6, -1/6, -1/2, 1/2, -1/3, 1/3, -1/6, 1/6 }

1/2

x

1/2

6*x^3+11*x^2-1 = 2.5

1/2

-1/2

x

-1/2

6*x^3+11*x^2-1 = 1

-1/2

1/3

x

1/3

6*x^3+11*x^2-1 = 0.44444444

1/3

-1/3

x

-1/3

6*x^3+11*x^2-1 = 0

-1/3

x+1/3

6*x^2+9*x-3

6*x^3+11*x^2-1

x+1/3

-6*x^3-2*x^2

9*x^2-1

-9*x^2-3*x

-3*x-1

3*x+1

0

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

DELTA = 9^2-(-3*4*6)

DELTA = 153

DELTA > 0

x = (153^(1/2)-9)/(2*6) or x = (-153^(1/2)-9)/(2*6)

x = (3*17^(1/2)-9)/12 or x = (-3*17^(1/2)-9)/12

x in { (-3*17^(1/2)-9)/12, (3*17^(1/2)-9)/12, -1/3}

x in { (-3*17^(1/2)-9)/12, (3*17^(1/2)-9)/12, -1/3 }

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