Réponse :
Bonjour
1) g(x) = x² + 10x + 9
g(-7) = (-7)² +10(-7) + 9 = 49 - 70 + 9 = -12
g(3/4) = (3/4)² +10(3/4) + 9 = 9/16 + 30/4 + 9 = 129/16 + 9 = 273/16
g(√2) = (√2)² + 10√2 + 9 = 10√2 + 11
2) (x + 5)² - 16 = x² + 10x + 25 - 16 = x² + 10x + 9 = g(x)
3) g(x) = (x + 5)² - 16 = (x + 5)² - 4² = (x + 5 + 4)(x + 5 - 4) = (x + 9)(x + 1)
4) a) g(x) = 0
⇔ (x + 9)(x + 1) = 0
⇔ x + 9 = 0 ou x + 1 = 0
⇔ x = -9 ou x = -1
S = {-9 ; -1}
b) g(x) = 9
⇔ x² + 10x + 9 = 9
⇔ x² + 10x = 0
⇔ x(x + 10) = 0
⇔ x = 0 ou x + 10 = 0
⇔ x = 0 ou x = -10
S = {-10 ; 0}
