(2-10x^2+8x^4)/((x^2+3)^2)

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Solution for (2-10x^2+8x^4)/((x^2+3)^2) equation: 


D( x )

(x^2+3)^2 = 0

(x^2+3)^2 = 0

(x^2+3)^2 = 0

1*x^2 = -3 // : 1

x^2 = -3

x in (-oo:+oo)

(8*x^4-(10*x^2)+2)/((x^2+3)^2) = 0

(8*x^4-10*x^2+2)/((x^2+3)^2) = 0

8*x^4-10*x^2+2 = 0

2*(4*x^4-5*x^2+1) = 0

4*x^4-5*x^2+1 = 0

{ 1, -1 }

1

x = 1

4*x^4-5*x^2+1 = 0

1

x-1

4*x^3+4*x^2-x-1

4*x^4-5*x^2+1

x-1

4*x^3-4*x^4

4*x^3-5*x^2+1

4*x^2-4*x^3

1-x^2

x^2-x

1-x

x-1

0

4*x^3+4*x^2-x-1 = 0

{ 1, -1 }

1

x = 1

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

1

-1

x = -1

4*x^3+4*x^2-x-1 = 0

-1

x+1

4*x^2-1

4*x^3+4*x^2-x-1

x+1

-4*x^3-4*x^2

-x-1

x+1

0

4*x^2-1 = 0

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

DELTA = 16

DELTA > 0

x = (16^(1/2)+0)/(2*4) or x = (0-16^(1/2))/(2*4)

x = 1/2 or x = -1/2

x in { -1/2, 1/2, 1, -1} 

2*(x+1/2)*(x-1/2)*(x-1)*(x+1) = 0

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

( x+1/2 )

x+1/2 = 0 // - 1/2

x = -1/2

( x+1 )

x+1 = 0 // - 1

x = -1

( x-1/2 )

x-1/2 = 0 // + 1/2

x = 1/2

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -1/2, -1, 1/2, 1 }

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