Réponse :
Bonsoir
a) A(1/2) = (1/2)² - 7×1/2 + 10 = 1/4 - 7/2 + 10 = 1/4 - 14/4 + 40/4 = 27/4
A(4/3) = (4/3)² - 7×4/3 + 10 = 16/9 - 28/3 + 10 = 16/9 - 84/9 + 90/9 = 22/9
b) A(√2) = (√2)² - 7√2 + 10 = 2 - 7√2 + 10 = 12 - 7√2
A(3-√2) = (3-√2)² - 7(3-√2) + 10 = 9 - 6√2 + 2 - 21 + 7√2 + 10 = √2
c) (x - 2)(x - 5) = x² - 5x - 2x + 10 = x² - 7x + 10 = A(x)
d) A(x) = 0 ⇔ (x - 2)(x - 5) = 0
⇔ x - 2 = 0 ou x - 5 = 0
⇔ x = 2 ou x = 5
S = {2 ; 5}