(3x^4-9x^2+6)/(x^2+6)

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Solution for (3x^4-9x^2+6)/(x^2+6) equation: 


D( x )

x^2+6 = 0

x^2+6 = 0

x^2+6 = 0

1*x^2 = -6 // : 1

x^2 = -6

x in (-oo:+oo)

(3*x^4-(9*x^2)+6)/(x^2+6) = 0

(3*x^4-9*x^2+6)/(x^2+6) = 0

3*x^4-9*x^2+6 = 0

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

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

{ 1, -1, 2, -2 }

1

x = 1

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

1

x-1

x^3+x^2-2*x-2

x^4-3*x^2+2

x-1

x^3-x^4

x^3-3*x^2+2

x^2-x^3

2-2*x^2

2*x^2-2*x

2-2*x

2*x-2

0

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

{ 1, -1, 2, -2 }

1

x = 1

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

1

-1

x = -1

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

-1

x+1

x^2-2

x^3+x^2-2*x-2

x+1

-x^3-x^2

-2*x-2

2*x+2

0

x^2-2 = 0

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

DELTA = 8

DELTA > 0

x = (8^(1/2)+0)/(1*2) or x = (0-8^(1/2))/(1*2)

x = 2^(1/2) or x = -2^(1/2)

x in { -2^(1/2), 2^(1/2), 1, -1} 

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x+2^(1/2) )

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

x = -2^(1/2)

( x-1 )

x-1 = 0 // + 1

x = 1

( x-2^(1/2) )

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

x = 2^(1/2)

x in { -1, -2^(1/2), 1, 2^(1/2) }

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