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Meilleure réponse !
2014-01-25T20:39:03+01:00
Exercice 49
a) (3x+4)(2x-1)+(3x+4)(x+9) = 0
(3x+4)(2x-1+x+9) = 0
(3x+4)(3x+8) = 0
d'où
3x+4 = 0
3x = -4
x = -4/3
ou
3x+8 = 0
3x = -8
x = -8/3
l'équation admet 2 solutions x= -4/3 et x = -8/3

b) (7x-8)(3x+2)+(7x-8)(6x+7) = 0
(7x-8)(3x+2+6x+7) = 0
(7x-8)(3x+2+6x+7) = 0
(7x-8)(9x+9) = 0
d'où
7x-8 = 0
7x = 8
x = 8/7
ou
9x+9 = 0
9x = -9
x = -9/9
x = -1
l'équation admet 2 solutions x= 8/7 et x = -1

c)(-x+4)(2x+2)+(-x+4)(-4x+2) = 0
(-x+4)(2x+2-4x+2) = 0
(-x+4)(-2x+4) = 0
(-x+4)()2 = 0
d'où
-x+4 = 0
x = 4
ou
-2x+4 = 0
-2x = -4
x = -4/-2
x = 2
l'équation admet 2 solutions x= 4 et x = 2

d) (10x-9)(-5x+2)+(10x-9)(2x+1) = 0
(10x-9)(-5x+2+2x+1) = 0
(10x-9)(-3x+3) = 0
d'où
10x-9 = 0
10x = 9
x = 9/10
ou
-3x+3 = 0
-3x = -3
x = -3/-3
x = 1
l'équation admet 2 solutions x= 9/10 et x = 1

Exercice 52
1) A = (x+5)(2x-4)+(x+5)(6x+2)
A = 2x²-4x+10x-20+6x²+2x+30x+10
A = 8x²+38x-10

2) A = (x+5)(2x-4)+(x+5)(6x+2)
A = (x+5)(2x-4+6x+2)
A = (x+5)(8x-2)

3) (x+5)(8x-2) = 0
L'équation égal 0 si :
x+5 = 0
x = -5
ou
8x-2 = 0
8x = 2
x = 2/8
x = 1/4
L'équation admet 2 solutions, x = -5 et x = 1/4