Réponse :
Bonsoir
1) f(x) = 2(x - 5)² - 18 = 2(x² - 10x + 25) - 18 = 2x² - 20x + 50 - 18
f(x) = 2x² - 20x + 32
2) f(x) = 2(x - 5)² - 18 = 2(x - 5)² - 2×3² = 2((x - 5)² - 3²)
f(x) = 2(x - 5 - 3)(x - 5 + 3) = 2(x - 8)(x - 2)
3) a) f(x) = 0
⇔ 2(x - 8)(x - 2) = 0
⇔ x - 8 = 0 ou x - 2 = 0
⇔ x = 8 ou x = 2
S = {2 ; 8}
b) f(5 + √3) = 2(5 + √3 - 5)² - 18 = 2(√3)² - 18 = 6 - 18 = -12
