Bonjour
D = (3x + 1)(6x - 9) - (2x - 3)^2
1) developper :
D = 18x^2 - 27x + 6x - 9 - (4x^2 - 12x + 9)
D = 18x^2 - 21x - 9 - 4x^2 + 12x - 9
D = 14x^2 - 9x - 18
2) calculer D pour x = 3/2 et x = V2 :
D = 14 * (3/2)^2 - 9 * 3/2 - 18
D = 14 * 9/4 - 27/2 - 18
D = 63/2 - 27/2 - 36/2
D = 0
D = 14 * (V2)^2 - 9 * V2 - 18
D = 14 * 2 - 9V2 - 18
D = 28 - 18 - 9V2
D = 10 - 9V2
3) factoriser 6x - 9, puis factoriser D :
6x - 9 = 3 * 2x - 3 * 3 = 3(2x - 3)
D = (3x + 1)(6x - 9) - (2x - 3)^2
D = (3x + 1) * 3(2x - 3) - (2x - 3)^2
D = (2x - 3)[3(3x + 1) - 2x + 3]
D = (2x - 3)(9x + 3 - 2x + 3)
D = (2x - 3)(7x + 6)
En déduire les solutions de D = 0 :
2x - 3 = 0 ou 7x + 6 = 0
2x = 3 ou 7x = -6
x = 3/2 ou x = -6/7
