Réponse :
Bonjour
1) développons f(x)
f(x) = (3x - 2)² - 9 = 9x² - 12x + 4 - 9 = 9x² - 12x - 5
Factorisons f(x)
f(x) = (3x - 2)² - 9 = (3x - 2)² - 3² = (3x - 2 + 3)(3x - 2 - 3) = (3x + 1)(3x - 5)
2) a) f(√2) = 9×(√2)² - 12×√2 - 5 = 18 - 12√2 - 5 = 13 - 12√2 ≈ -3,97
b) f(x) = 0 ⇔ (3x - 5)(3x + 1) = 0 ⇔ 3x - 5 = 0 ou 3x + 1 = 0
⇔ 3x = 5 ou 3x = -1 ⇔ x = 5/3 ou x = -1/3
S = {-1/3 ; 5/3}
c) f(x) = -5 ⇔ 9x² - 12x - 5 = -5 ⇔ 9x² - 12x = 0 ⇔ x(9x - 12) = 0
⇔ x = 0 ou 9x - 12 = 0 ⇔ x = 0 ou 9x = 12 ⇔ x = 0 ou x =12/9 = 4/3
S = {0 ; 4/3}
