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Rimasoundousss
@Rimasoundousss
April 2019
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Bonsoir ! Aidez moi svp
Exercice 1 :
1) Ecrire 17 et 2005 comme différence de deux carrés consécutifs .
2) Vérifier que
est impair puis écrivez le comme différence de deux carrés consécutifs .
Exercice 2 :
SOit a et b deux entiers naturels impairs
Montrer que 8 divise
merci d'avance
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Verified answer
17 = (n+1)² - n² = n² + 2n +1 - n² = 2n +1 = 2 *8 +1 n=8
17 = 9² - 8² = 81 - 64
2005 = 2n +1 = 2*1002 +1 n = 1002
2005 = 1003² - 1002² = 1006009 - 1004004 = 2005
2) n² + n = n(n+1) est toujours pair ( n ou n+1 est forcément pair)
7 est impair
un pair plus un impair = un impair n² +n +7 est toujours impair
n² + n + 7 = (p+1)² - p² = 2p +1 n² + n +6 = 2p
p = (n² +n) /2 + 3
n² + n +7 =( ( n²+n ) /2 + 4 )² - ( (n² + n) /2 + 3 )²
ex2
non
a = 3 b =5 a² +b² -b =9 +25 - 5 = 29 pas divisible par 8
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Salut ... je veux bien de l'aide svp concernant cet exercice. .. c urgent. .. mrc d'avance.
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Verified answer
17 = (n+1)² - n² = n² + 2n +1 - n² = 2n +1 = 2 *8 +1 n=817 = 9² - 8² = 81 - 64
2005 = 2n +1 = 2*1002 +1 n = 1002
2005 = 1003² - 1002² = 1006009 - 1004004 = 2005
2) n² + n = n(n+1) est toujours pair ( n ou n+1 est forcément pair)
7 est impair
un pair plus un impair = un impair n² +n +7 est toujours impair
n² + n + 7 = (p+1)² - p² = 2p +1 n² + n +6 = 2p
p = (n² +n) /2 + 3
n² + n +7 =( ( n²+n ) /2 + 4 )² - ( (n² + n) /2 + 3 )²
ex2
non
a = 3 b =5 a² +b² -b =9 +25 - 5 = 29 pas divisible par 8