Exercice 1:
a)
(4x-3) (2+x) = (2x-3)²
8x + 4x² -6 -3x = 4x² -12x +9
4x² + 5x -6 = 4x² -12x +9
4x² -4x² +5x +12x = 9 + 6
17x = 15
x= 15/17
b)
3/4 - (2x-5)/3 = (x-3)/6
9/12 - 4(2x-5)/12 = 2(x-3)/12
9/12 - (8x -20)/12 = (2x -6)/12
(9 -8x +20) /12 = (2x -6)/12
(-8x +29)/12 - (2x-6)/12 = 0
(-8x +29 -2x +6)/12 = 0
(-10x +35)/12 = 0
-10x +35 = 0*12
-10x = -35
x= 35/10
x= 7/2
c)
(7x +2)² = 49
(7x +2)² -7² = 0
(7x +2 -7) (7x +2 +7) = 0
(7x -5) (7x +9) = 0
On applique la règle du produit nul:
7x -5 = 0 ou 7x +9 = 0
7x = 5 ou 7x = -9
x= 5/7 ou x= -9/7
d)
(9 -5x)² = (9 -5x) (6x+1)
(9-5x)² - (9-5x) (6x+1) = 0
(9-5x) (9 -5x -6x -1) = 0
(9-5x) (-11x +8) =0
On applique la règle du produit nul:
9 -5x = 0 ou -11x +8 = 0
-5x = -9 ou -11x = -8
x= 9/5 ou x= 8/11
Voilà ! J'espère t'avoir aidé(e) ! :)
