(48a^4-16a^2-32)/(8a^2-8)

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Solution for (48a^4-16a^2-32)/(8a^2-8) equation:


D( a )

8*a^2-8 = 0

8*a^2-8 = 0

8*a^2-8 = 0

8*a^2 = 8 // : 8

a^2 = 1

a^2 = 1 // ^ 1/2

abs(a) = 1

a = 1 or a = -1

a in (-oo:-1) U (-1:1) U (1:+oo)

(48*a^4-(16*a^2)-32)/(8*a^2-8) = 0

(48*a^4-16*a^2-32)/(8*a^2-8) = 0

48*a^4-16*a^2-32 = 0

16*(3*a^4-a^2-2) = 0

3*a^4-a^2-2 = 0

{ 1, -1, 2, -2 }

1

a = 1

3*a^4-a^2-2 = 0

1

a-1

3*a^3+3*a^2+2*a+2

3*a^4-a^2-2

a-1

3*a^3-3*a^4

3*a^3-a^2-2

3*a^2-3*a^3

2*a^2-2

2*a-2*a^2

2*a-2

2-2*a

0

3*a^3+3*a^2+2*a+2 = 0

{ 1, -1, 2, -2 }

1

a = 1

3*a^3+3*a^2+2*a+2 = 10

1

-1

a = -1

3*a^3+3*a^2+2*a+2 = 0

-1

a+1

3*a^2+2

3*a^3+3*a^2+2*a+2

a+1

-3*a^3-3*a^2

2*a+2

-2*a-2

0

3*a^2+2 = 0

DELTA = 0^2-(2*3*4)

DELTA = -24

DELTA < 0

a in { 1, -1}

16*(a-1)*(a+1) = 0

(16*(a-1)*(a+1))/(8*a^2-8) = 0

( 16 )

16 = 0

a belongs to the empty set

( a+1 )

a+1 = 0 // - 1

a = -1

( a-1 )

a-1 = 0 // + 1

a = 1

a in { -1}

a in { 1}

a belongs to the empty set

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