(65536-16384x+1536x^2-64x^3+x^4)/(x^2-4)

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Solution for (65536-16384x+1536x^2-64x^3+x^4)/(x^2-4) equation: 


D( x )

x^2-4 = 0

x^2-4 = 0

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in (-oo:-2) U (-2:2) U (2:+oo)

(x^4-(64*x^3)+1536*x^2-(16384*x)+65536)/(x^2-4) = 0

(x^4-64*x^3+1536*x^2-16384*x+65536)/(x^2-4) = 0

x^4-64*x^3+1536*x^2-16384*x+65536 = 0

x^4-64*x^3+1536*x^2-16384*x+65536 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64, 128, -128, 256, -256, 512, -512, 1024, -1024, 2048, -2048, 4096, -4096, 8192, -8192, 16384, -16384, 32768, -32768, 65536, -65536 }

1

x = 1

x^4-64*x^3+1536*x^2-16384*x+65536 = 50625

1

-1

x = -1

x^4-64*x^3+1536*x^2-16384*x+65536 = 83521

-1

2

x = 2

x^4-64*x^3+1536*x^2-16384*x+65536 = 38416

2

-2

x = -2

x^4-64*x^3+1536*x^2-16384*x+65536 = 104976

-2

4

x = 4

x^4-64*x^3+1536*x^2-16384*x+65536 = 20736

4

-4

x = -4

x^4-64*x^3+1536*x^2-16384*x+65536 = 160000

-4

8

x = 8

x^4-64*x^3+1536*x^2-16384*x+65536 = 4096

8

-8

x = -8

x^4-64*x^3+1536*x^2-16384*x+65536 = 331776

-8

16

x = 16

x^4-64*x^3+1536*x^2-16384*x+65536 = 0

16

x-16

x^3-48*x^2+768*x-4096

x^4-64*x^3+1536*x^2-16384*x+65536

x-16

16*x^3-x^4

1536*x^2-48*x^3-16384*x+65536

48*x^3-768*x^2

768*x^2-16384*x+65536

12288*x-768*x^2

65536-4096*x

4096*x-65536

0

x^3-48*x^2+768*x-4096 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64, 128, -128, 256, -256, 512, -512, 1024, -1024, 2048, -2048, 4096, -4096 }

1

x = 1

x^3-48*x^2+768*x-4096 = -3375

1

-1

x = -1

x^3-48*x^2+768*x-4096 = -4913

-1

2

x = 2

x^3-48*x^2+768*x-4096 = -2744

2

-2

x = -2

x^3-48*x^2+768*x-4096 = -5832

-2

4

x = 4

x^3-48*x^2+768*x-4096 = -1728

4

-4

x = -4

x^3-48*x^2+768*x-4096 = -8000

-4

8

x = 8

x^3-48*x^2+768*x-4096 = -512

8

-8

x = -8

x^3-48*x^2+768*x-4096 = -13824

-8

16

x = 16

x^3-48*x^2+768*x-4096 = 0

16

x-16

x^2-32*x+256

x^3-48*x^2+768*x-4096

x-16

16*x^2-x^3

768*x-32*x^2-4096

32*x^2-512*x

256*x-4096

4096-256*x

0

x^2-32*x+256 = 0

DELTA = (-32)^2-(1*4*256)

DELTA = 0

x = 32/(1*2)

x = 16 or x = 16

x in { 16, 16, 16, 16} 

(x-16)^4 = 0

((x-16)^4)/(x^2-4) = 0

x-16 = 0 // + 16

x = 16

x in { 16, 16, 16, 16 }

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