bonjour,
trop long, sépare
exo 5 :
109*91 = (100+9)(100-9) =(a+b)(a-b) = a²-b² = 100²-9² = 10 000-81 =9919
125²-75² = (100+25)(100-25) =(a+b)(a-b) = 100²-25² = 10 000-625 = ....
103² = (100+3)² =(a+b)² =a²+2ab+b² = 100²+600+9 = .....
exo 6 :
1) A ABCD : (2x+1)(3x-5)
2) A EFGHI : (3x-7)²-2² =
(3x-7-2)(3x-7+2) =
(3x-9)(3x-5)
3) (2x+1)(3x-5) = (3x-9)(3x-5)
(2x+1)(3x-5) -(3x-9)(3x-5) = 0
(3x-5)(2x+1-3x+9) = 0
(3x-5)(x+10) = 0
3x-5 =0
3x = 5
x = 5/3
x=10 = 0
x = -10
pour x =5/3 les 2aires sont =
vérif :
A ABCD = (2x+1)(3x-5) = 6x²-10x+3x-5 = 6x²-7x-5
6(5/3)² -7*5/3- 5 =
6*25/9 - 35/3 -5 = 0
A (3x-7)²-2² = 9x²-42x+49-4 = 9x²-42x+45 =
9(5/3)² - 42*5/3 + 45=
225/9 -210/3 + 45 = 0
pour x =5/3 le figure n'existe pas
