Öva konjugatregeln
Definition: (a+b)(a-b) = a2-ab+ab-b2= a2 -b2 Exempel: (x+4)(x-4) = x2-42 = x2-16
Använd konjugatregeln som i exemplet ovan
=
− +1)( 1)
(x x ______________________________________________
=
− +2)( 2)
(x x ________________________________________________
=
− +5)( 5)
(x x __________________________________________
=
− +10)( 10)
(x x __________________________________________
=
− +1)(2 1) 2
( x x _____________________________________
=
− +5)(2 5) 2
( x x _____________________________________
=
− +4)( 4)
(x2 x2 _____________________________________
=
−
+ )( )
(x2 x x2 x _____________________________________
= + +2)( 2)
(x x _____________________________________________
=
− +5)( 7)
(x x _____________________________________________
= +
− +2)( 2)
(x x _____________________________________________
= +
−2)( 2)
(x x _____________________________________________
Använd konjugatregeln ”baklänges”
=
−1
x2 __________________________________________________
=
− 9
x2 _________________________________________________
=
− 2
16 x ________________________________________________
=
− 81
9x2 __________________________________________________
Facit
1 )
1 )(
1
(x+ x− = x2 −
4 )
2 )(
2
(x+ x− = x2−
25 )
5 )(
5
(x+ x− =x2 −
100 )
10 )(
10
(x+ x− = x2 −
1 4 ) 1 2 )(
1 2
( x+ x− = x2 −
25 4
) 5 2 )(
5 2
( x+ x− = x2 −
16 )
4 )(
4
(x2+ x2 − = x4−
2 4 2
2 )( )
(x +x x −x = x −x
4 4 )
2 ( ) 2 )(
2
(x+ x+ = x+ 2 = x2+ x+
35 2 35
5 7 )
7 )(
5
(x+ x− = x2 − x+ x− = x2 − x−
4 2
) 2 )(
2 ( ) 2 )(
2
(x+ −x+ = +x −x = −x
4 )
2 )(
2 ( ) 2 )(
2
(x− x+ = x+ x− = x2 −
Använd konjugatregeln ”baklänges”
) 1 )(
1 (
2−1= x+ x−
x
) 3 )(
3 (
2−9= x+ x−
x
) 4 )(
4 (
16−x2 = +x −x
) 9 3 )(
9 3 ( 81
9x2− = x+ x−
