Réponse :
Explications étape par étape
Bonjour
(-b) x c | a^2 ...| (-b) x d
d^2 ......| a x b | c^2
a x (-c) | b^2 ...| -a x d
Peut on choisir les nombres suivants :
a = -2 ; b = 10 ; c = -4 ; d = -5
a x b = c x d
-2 x 10 = -20
-4 x -5 = 20
Non
a = -4 ; b = 3 ; c = 2 ; d = -6
-4 x 3 = -12
2 x -6 = -12
Oui
Si oui construire le carré magique associé :
a = -4 ; b = 3 ; c = 2 ; d = -6
(-b) x c | a^2 ...| (-b) x d
d^2 ......| a x b | c^2
a x (-c) | b^2 ...| -a x d
(-b) x c = -3 x 2 = -6
a^2 = (-4)^2 = 16
(-b) x d = -3 x (-6) = 18
d^2 = (-6)^2 = 36
a x b = -4 x 3 = -12
c^2 = 2^2 = 4
a x (-c) = -4 x (-2) = 8
b^2 = 3^2 = 9
-a x d = -(-4) x (-6) = -24
-6 | 16 | 18
36| -12| 4
8 | 9...| -24
-6 x 16 x 18 = -1728
36 x -12 x 4 = -1728
8 x 9 x -24 = -1728
-6 x 36 x 8 = -1728
16 x -12 x 9 = -1728
18 x 4 x -24 = -1728
-6 x -12 x -24 = -1728
18 x -12 x 8 = -1728
