a) (8x+10)(10x+9)=0 -...

Exercice 9 page 140

a) (8x+ 10)(10x+ 9) = 0

Résoudre l’équation avant de lire la solution sur la page suivante

Exercice 9 page 140

a) (8x+ 10)(10x+ 9) = 0

8x+ 10 = 0 ou 10x+ 9 = 0

8x = −10 ou 10x = −9

x = −10

8ou x = − 9

10

x = −1, 25 ou x = −0, 9 S = {−1, 25;−0, 9}

Exercice 9 page 140

b) (5− 3x)(2x− 5) = 0


Exercice 9 page 140

b) (5− 3x)(2x− 5) = 0

5− 3x = 0 ou 2x− 5 = 0

5 = 3x ou 2x = 5

x =5

3ou x =

5

2S =

{

5

3;5

2

}

Exercice 9 page 140

c) (3− 8x)(8x− 8) = 0


Exercice 9 page 140

c) (3− 8x)(8x− 8) = 0

3− 8x = 0 ou 8x− 8 = 0

3 = 8x ou 8x = 8

x =3

8ou x =

8

8= 1 S =

{

3

8; 1

}

Exercice 9 page 140

d) (2x+ 5)(6x− 1) = 0


Exercice 9 page 140

d) (2x+ 5)(6x− 1) = 0

2x+ 5 = 0 ou 6x− 1 = 0

2x = −5 ou 6x = 1

x = −5

2ou x =

1

6S =

{

5

2;1

6

}

Exercice 9 page 140

e) 3(6x− 8)(7x+ 9) = 0


Exercice 9 page 140

e) 3(6x− 8)(7x+ 9) = 0

6x+ 8 = 0 ou 7x+ 9 = 0

6x = −8 ou 7x = −9

x = −8

6= −4

3ou x = −9

7S =

{

−4

3;−9

7

}

Exercice 9 page 140

f) 6(2x− 4)(4x− 7) = 0


Exercice 9 page 140

f) 6(2x− 4)(4x− 7) = 0

2x− 4 = 0 ou 4x− 7 = 0

2x = 4 ou 4x = 7

x =4

2= 2 ou x =

7

4S =

{

2;7

4

}

Exercice 11 page 140

6x2 − 4x = 0



6x2 − 4x = 0

2x(3x− 4) = 0

2x = 0 ou 3x− 4 = 0

x = 0 ou 3x = 4

x = 0 ou x =4

3S =

{

0;4

3

}


a) 4x2 − 4x+ 1 = 0



a) 4x2 − 4x+ 1 = 0

Il faut reconnaître une identité remarquable :

(2x)2 − 2× 2x+ 1 = 0

(2x− 1)2 = 0

2x− 1 = 0

2x = 1

x =1

2S =

{

1

2

}


b) 9x2 − 25 = 0



b) 9x2 − 25 = 0


(3x)2 − 52 = 0

(3x− 5)(3x+ 5) = 0

3x− 5 = 0 ou 3x+ 5 = 0

3x = 5 ou 3x = −5 S =

{

−5

3;5

3

}


c) 16x2 − 80x+ 100 = 0



c) 16x2 − 80x+ 100 = 0


(4x)2 − 2× 4x× 10 + 1 = 0

(4x− 10)2 = 0

4x− 10 = 0

4x = 10

x =10

4= 2, 5 S = {2, 5}


d) 100x2 − 36 = 0



d) 100x2 − 36 = 0


(10x)2 − 62 = 0

(10x− 6)(10x+ 6) = 0

10x− 6 = 0 ou 10x+ 6 = 0

10x = 6 ou 10x = −6

x =6

10= 0, 6 ou x = − 6

10= −0, 6 S = {−0, 6; 0, 6}


e) 16x2 − 48x+ 36 = 0



e) 16x2 − 48x+ 36 = 0


(4x)2 − 2× 4x× 6 + 1 = 0

(4x− 6)2 = 0

4x− 6 = 0

4x = 6

x =6

4= 1, 5 S = {1, 5}


f) 16x2 + 24x+ 9 = 0



f) 16x2 + 24x+ 9 = 0


(4x)2 + 2× 4x× 3 + 32 = 0

(4x+ 3)2 = 0

4x+ 3 = 0

4x = −3

x = −3

4S =

{

−3

4

}


a) x2 = 36



a) x2 = 36

x2 − 62 = 0

(x+ 6)(x− 6) = 0

x+ 6 = 0 ou x− 6 = 0

x = −6 ou x = 6 S = {−6; 6}


b) x2 = 8



b) x2 = 8

x2 − (2

√2)2 = 0

(x+ 2√2)(x− 2

√2) = 0

x = −2√2 ou x = 2

√2

S ={

−2√2; 2

√2}


c) x2 = −81



c) x2 = −81

Le carré d’un nombre réel est toujours positif ou nul

S = ∅


d) x2 − 87 = −5



d) x2 − 87 = −5

x2 − 82 = 0

x2 − (

√82)2

(x+√82)(x−

√82) = 0

x = −√82 ou x =

√82

S ={

−√82;

√82}


e) (x+ 10)2 = 9



e) (x+ 10)2 = 9

(x+ 10)2 − 32 = 0

(x+ 10− 3)(x+ 10 + 3) = 0

(x+ 7)(x+ 13) = 0

x+ 7 = 0 ou x+ 13 = 0

x = −7 ou x = −13 S = {−13;−7}


f) (x− 8)2 − 18 = −2



f) (x− 8)2 − 18 = −2

(x− 8)2 − 16 = 0

(x− 8)2 − 42 = 0

(x− 8− 4)(x− 8 + 4) = 0

(x− 12)(x− 4) = 0

x− 12 = 0 ou x− 4 = 0

x = 12 ou x = 4 S = {4; 12}


a) (1 + 4x)2 − (5x− 2)(1 + 4x) = 0



a) (1 + 4x)2 − (5x− 2)(1 + 4x) = 0

(1 + 4x) [(1 + 4x)− (5x− 2)] = 0

(1 + 4x)(1 + 4x− 5x+ 2) = 0

(1 + 4x)(−x + 3) = 0

1 + 4x = 0 ou − x+ 3 = 0

4x = −1 ou 3 = x donc x = −1

4ou x = 3 S =

{

−1

4; 3

}


b) (9x+ 1)2 = (x+ 5)2



b) (9x+ 1)2 = (x+ 5)2

(9x+ 1)2 − (x+ 5)2 = 0

[(9x+ 1) + (x+ 5)] [(9x+ 1)− (x+ 5)] = 0

(9x+ 1 + x+ 5)(9x+ 1− x− 5) = 0

(10x+ 6)(8x− 4) = 0 donc 10x+ 6 = 0 ou 8x− 4 = 0

10x = −6 ou 8x = 4

x = − 6

10= −0, 6 ou x =

4

8= 0, 5 S = {−0, 6; 0, 5}


c) 9− 4x2 − (5− x)(3− 2x) = 0



c) 9− 4x2 − (5− x)(3− 2x) = 0

(3− 2x)(3 + 2x)− (5− x)(3 − 2x) = 0

(3− 2x) [(3 + 2x)− (5− x)] = 0

(3− 2x)(3 + 2x− 5 + x) = 0

(3− 2x)(3x− 2) = 0

3− 2x = 0 ou 3x− 2 = 0

3 = 2x ou 3x = 2

x =3

2ou x =

2

3S =

{

2

3;3

2

}

a) (8x+10)(10x+9)=0 -...

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