1.5 1) 8x +6x=9
8x 2
+6x 9=0
=6 2
48( 9)=324=18 2
>0
x
1
= 6 18
28
= 24
16
= 3
2
et x
2
= 6+18
28
= 12
16
= 3
4
S=
3
2
; 3
4
2) 2x 2
x+1=0
=( 1) 2
421= 7<0
S=?
3) x 2
+4 6x=0
x 2
6x+4=0
=( 6) 2
414=20>0
p
= p
20= p
2 2
5=2 p
5
x
1
=
( 6) 2 p
5
21
= 6 2
p
5
2
= 6
2 2
p
5
2
=3 p
5
x
2
=
( 6)+2 p
5
21
= 6+2
p
5
2
= 6
2 +
2 p
5
2
=3+ p
5
S=f3 p
5;3+ p
5g
4) 9x 2
30x+25=0
=( 30) 2
4925=0
x= ( 30)
29
= 30
18
= 5
3
S=
5
3
5) x 2
6x+7=0
=( 6) 2
417=8>0 p
= p
8= p
2 2
2=2 p
2
x
1
=
( 6) 2 p
2
21
= 6 2
p
2
2
= 6
2 2
p
2
2
=3 p
2
x
2
=
( 6)+2 p
2
21
= 6+2
p
2
2
= 6
2 +
2 p
2
2
=3+ p
2
S=f3 p
2;3+ p
2g
6) x
2
3
2
x 2
+1
3
= x
2
11
6
6
3(x 2
3) 2(x 2
+1)=x 2
11
3x 2
9 2x 2
2=x 2
11
0=0
S=R, ar l'équation0=0est vériée quel quesoit x2R.
7) x= 2
5 +
5x
16
80
80x=32+25x 2
25x 2
80x+32=0
=( 80) 2
42532=3200
p
= p
3200= p
10 2
32=10 p
32=10 p
4 2
2=104 p
2=40 p
2
x
1
=
( 80) 40 p
2
225
= 80 40
p
2
50
= 80
50 40
p
2
50
= 8
5 4
p
2
5
= 8 4
p
2
5
x
2
=
( 80)+40 p
2
225
= 80+40
p
2
50
= 80
50 +
40 p
2
50
= 8
5 +
4 p
2
5
= 8+4
p
2
5
S=
8 4 p
2
5
; 8+4
p
2
5
8)
(x 2) 2
5
(x 3) 2
4
=0 20
4(x 2) 2
5(x 3) 2
=0
4(x 2
4x+4) 5(x 2
6x+9)=0
4x 2
16x+16 5x 2
+30x 45=0
x 2
+14x 29=0 ( 1)
x 2
14x+29=0
=( 14) 2
4129=80 p
= p
80= p
4 2
5=4 p
5
x
1
=
( 14) 4 p
5
21
= 14 4
p
5
2
= 14
2 4
p
5
2
=7 2 p
5
x
2
=
( 14)+4 p
5
21
= 14+4
p
5
2
= 14
2 +
4 p
5
2
=7+2 p
5
S=f7 2 p
5;7+2 p
5g
