Réponse:
Exercice 2 :
1) x² -4x = 0
x × (x -4) = 0
x = 0
x -4 = 0
x = 4
L'équation a deux solutions : 0 ou 4 .
2) 3x² -9x = 0
x(3x - 9) = 0
x = 0
3x -9 = 0
3x = 9
3x/3 = 9/3
x = 3
L'équation a deux solutions : 0 ou 3 .
3) 4x² = 3x
4x² -3x = 0
x × (4x -3) = 0
x = 0
4x -3 = 0
4x = 3
4x/4 = 3/4
x = 3/4
L'équation a deux solutions : 0 ou 3/4
4) x = x²
x -x² = 0
x × (1 -x) = 0
x = 0
1 -x = 0
-x = -1
x = 1
L'équation a deux solutions : 0 ou 1 .
5) 3x² -5 = 5x² -5 +3x
3x² -5x² -3x = -5 +5
-2x² -3x = 0
-x(2x +3) = 0
-x = 0
x = 0
2x +3 = 0
2x = -3
2x/2 = -3/2
x = -3/2
L'équation a deux solutions : 0 ou -3/2 .
Exercice 3 :
1) (x -2)(2x -1) + (x -2)(3x -4) = 0
(x -2)(2x -1 +3x -4) = 0
(x -2)(5x -5) = 0
x -2 = 0
x = 2
5x -5 = 0
5x = 5
5x/5 = 5/5
x = 1
L'équation a deux solutions : 2 ou 1 .
2) (3x -2)(5x -1) - (3x -2)(3x +4) = 0
(3x -2)(5x -1 -(3x+4))= 0
(3x -2)(5x -1 -3x -4) = 0
(3x -2)(2x -5) = 0
3x -2 = 0
3x = 2
3x/3 = 2/3
x = 2/3
2x -5 = 0
2x = 5
2x/2 = 5/2
x = 5/2
L'équation a deux solutions : 2/3 ou 5/2
3) (2x -1)2 - (x -5)(2x -1) = 0
(2x -1)(2 -(x-5)) = 0
(2x -1)(2 -x +5) = 0
(2x -1)(7 -x) = 0
2x -1 = 0
2x = 1
2x/2 = 1/2
x = 1/2
7 -x = 0
-x = -7
x = 7
L'équation a deux solutions : 1/2 ou 7 .
