Bonsoir
Résoudre :
1. (5x-1)(3x-2)+(6x-4)(x-1)=0
(5x - 1)(3x - 2) + 2(3x - 2)(x - 1) = 0
(3x - 2)(5x - 1 + 2(x - 1)) = 0
(3x - 2)(5x - 1 + 2x - 2) = 0
(3x - 2)(7x - 3) = 0
3x - 2 = 0 ou 7x - 3 = 0
3x = 2 ou 7x = 3
x = 2/3 ou x = 3/7
2. (3-2x)(2x+4)=(2x-3)(3-9X)
(3 - 2x)(2x + 4) + (3 - 2x)(3 - 9x) = 0
(3 - 2x)(2x + 4 + 3 - 9x) = 0
(3 - 2x)(-7x + 7) = 0
7(3 - 2x)(-x + 1) = 0
3 - 2x = 0 ou -x + 1 = 0
....
3. (6x-3)(1-2x)+(3-4x)(2-3x)=0
6x - 12x^2 - 3 + 6x + 6 - 9x^2 - 8x + 12x^2 = 0
-9x^2 + 4x + 3 = 0
[tex]\Delta = 4^{2} - 4 \times -9 \times 3 = 16 + 108 = 124[/tex]
X1 = [tex]\dfrac{-4-\sqrt124}{2 \times -9}[/tex]
X2 = [tex]\dfrac{-4+\sqrt124}{-18}[/tex]
