Bonsoir
On considère l'expression D (x) = (3x - 5)2 - (2x - 1) (3x - 5)
1-Développer et réduire D(x).
D (x) = (3x - 5)² - (2x - 1) (3x - 5)
D (x) = 9x² - 30x + 25 - (6x² - 10x - 3x + 5)
D (x) = 9x² - 30x + 25 - 6x² + 10x + 3x - 5
D (x) = 3x² - 17x + 20
2-Factoriser D(x).
D (x) = (3x - 5)² - (2x - 1) (3x - 5)
D (x) = (3x - 5) [(3x - 5) - (2x - 1)]
D (x) = (3x - 5) (3x - 5 - 2x + 1)
D (x) = (3x - 5) (x - 4)
-Résoudre D(x) = 0.
D (x) = (3x - 5) (x - 4) = 0
3x - 5 = 0 ou x - 4 = 0
3x = 5 x = 4
x = 5/3.
