Bonjour
On considère les trois expressions suivantes
A = (7x-3)² - (5x + 2)(6x-7)
B = (x-5)(6x +14) + (x-5)²
C = (4x-2)²- (3x+7)²
1. Démontrer que B=C
B = (x-5)(6x +14) + (x-5)²
B = 6x² + 14x - 30x - 70 + x² - 10x + 25
B = 6x² + x² + 14x - 30x - 10x - 70 + 25
B = 7x² - 26x - 45
C = (4x-2)²- (3x+7)²
C = 16x² - 16x + 4 - (9x² + 42x + 49)
C = 16x² - 16x + 4 - 9x² - 42x - 49
C = 16x² - 9x² - 16x - 42x + 4 - 49
C = 7x² - 58x - 45
B ≠ C
2. Peut-on dire que A=B ?
A = (7x-3)² - (5x + 2)(6x-7)
A = 49x² - 42x + 9 - (30x² - 35x + 12x - 14)
A = 49x² - 42x + 9 - 30x² + 35x - 12x + 14
A = 49x² - 30x² - 42x - 12x + 35x + 9 + 14
A = 19x² - 19x + 23
A ≠ B
3. Calculer A et B pour x=5
A = 19x² - 19x + 23
A = 19 * 5² - 19 * 5 + 23
A = 19 * 25 - 95 + 23
A = 475 - 95 + 23
A = 403
B = 7x² - 26x - 45
B = 7 * 5² - 26 * 5 - 45
B = 7 * 25 - 130 - 45
B = 175 - 175
B = 0
et x = -7
A = 19x² - 19x + 23
A = 19 * (- 7)² - 19 * (- 7) + 23
A = 19 * 49 + 133 + 23
A = 931 + 156
A = 1 087
B = 7x² - 26x - 45
B = 7 * (- 7)² - 26 * (- 7) - 45
B = 7 * 49 + 182 - 45
B = 343 + 137
B = 480.
