Bonjour,
1)
A (x) = (2x - 3)² - 1
A (x) = 4x² - 12x + 9 - 1
A (x) = 4x² - 12x + 8
2)
A (x) = (2x - 3)² - 1
A (x) = (2x - 3 - 1) (2x - 3 + 1)
A (x) = (2x - 4) (2x - 2)
A (x) = 4 (x - 2) (x - 1)
3) a)
A (x) = 0
x - 2 = 0 ou x - 1 = 0
x = 2 x = 1
2) 1-
B (x) = (x - 1)² + x² + (x + 1)²
B (x) = x² - 2x + 1 + x² + x² + 2x + 1
B (x) = x² + x² + x² - 2x + 2x + 1 + 1
B (x) = 3x² + 2
2-
(x - 1)² + x² + (x + 1)² = 1 325
x² - 2x + 1 + x² + x² + 2x + 1 = 1 325
x² + x² + x² - 2x + 2x + 1 + 1 = 1 325
3x² + 2 = 1 325
3x² = 1 325 - 2
3x² = 1 323
x² = 1 32/3
x² = 441
x = √441
x = 21
x - 1 = 21 - 1 = 20
x + 1 = 21 + 1 = 22
Ces nombres sont : 20 ; 21 et 22.
Vérification :
20² + 21² + 22² = 400 + 441 + 484 = 1 325
