x-256/x^3

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Solution for x-256/x^3 equation:


D( x )

x^3 = 0

x^3 = 0

x^3 = 0

1*x^3 = 0 // : 1

x^3 = 0

x = 0

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

x-(256/(x^3)) = 0

x-256*x^-3 = 0

1*x^1-256*x^-3 = 0

(1*x^4-256*x^0)/(x^3) = 0 // * x^6

x^3*(1*x^4-256*x^0) = 0

x^3

x^4-256 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64, 128, -128, 256, -256 }

1

x = 1

x^4-256 = -255

1

-1

x = -1

x^4-256 = -255

-1

2

x = 2

x^4-256 = -240

2

-2

x = -2

x^4-256 = -240

-2

4

x = 4

x^4-256 = 0

4

x-4

x^3+4*x^2+16*x+64

x^4-256

x-4

4*x^3-x^4

4*x^3-256

16*x^2-4*x^3

16*x^2-256

64*x-16*x^2

64*x-256

256-64*x

0

x^3+4*x^2+16*x+64 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64 }

1

x = 1

x^3+4*x^2+16*x+64 = 85

1

-1

x = -1

x^3+4*x^2+16*x+64 = 51

-1

2

x = 2

x^3+4*x^2+16*x+64 = 120

2

-2

x = -2

x^3+4*x^2+16*x+64 = 40

-2

4

x = 4

x^3+4*x^2+16*x+64 = 256

4

-4

x = -4

x^3+4*x^2+16*x+64 = 0

-4

x+4

x^2+16

x^3+4*x^2+16*x+64

x+4

-x^3-4*x^2

16*x+64

-16*x-64

0

x^2+16 = 0

DELTA = 0^2-(1*4*16)

DELTA = -64

DELTA < 0

x in { 4, -4}

x in { 4, -4 }

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