Exercice 13 :
1.
A = (2x - 1)² + (2x - 1) (-x-3)
A = (2x - 1) (2x - 1) + (2x - 1) (- x - 3)
A = (2x - 1) (2x - 1 - x - 3)
A = (2x - 1) (x - 4)
2.
A = (2x - 1) (x - 4)
A = 2x * x + 2x * (-4) - 1 * x - 1 * (-4)
A = 2x² - 8x - x - 4
A = 2x² - 9x - 4
Donc A = B
3.
B = 2x² - 9x - 4
B = 2 x (√5)² - 9 x (√5) - 4
B = 10 - 9√5 - 4
B = 6 - 9√5
4.
(2x - 1) (x - 4) = 0
Soit :
(2x - 1) = 0
donc 2x - 1 = 0
2x = 1
x = 1/2
ou soit : (x - 4) = 0
donc x - 4 = 0
x = 4
S = {1/2 ; 4}
