Bonjour,
a. x²≠ x → Fausse
b. (x + 3)2 + x2 = 2x2 + 6x + 9
x² + 6x + 9 + x² = 2x² + 6x + 9
2x² + 6x + 9 = 2x² + 6x + 9 → Vraie
c. (x - 1)(x - 2)(x - 4) = x² – 5x² + 8x - 4
(x² - 2x - x + 2) (x - 4) = x³ - 4x² - 2x² + 8x - x² + 4x + 2x - 8 = x³- 5x² + 14x - 8
x² - 5x² + 8x - 4 = - 4x² + 8x - 4
x³ - 5x² + 14x - 8 ≠ - 4x² + 8x - 4 → Fausse
d. 2x2 - 8x + 15 = 2(x - 2)2 + 7
2 (x - 2)² + 7 = 2 (x² - 4x + 4) + 7 = 2x² - 8x + 8 + 7 = 2x² - 8x + 15
2x² - 8x + 15 = 2x² - 8x + 15 → Vraie
e. (x + 5)(x - 3) = (x + 1)2 - 16
(x + 5) (x - 3) = x² - 3x + 5x - 15 = x² + 2x - 15
(x + 1)² - 16 = x² + 2x + 2 - 16 = x² + 2x - 14
x² + 2x - 15 ≠ x² + 2x - 14 → Fausse.
