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helloevery
@helloevery
January 2021
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Comment peut on déduire sans calculatrice le résultat de
999996² - 999999 X 1000003
Merci
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nonotata
Bonsoir,
999 996² = ( 1 000 000 - 4 )²
999 999 × 1 000 003 = ( 1 000 001 - 2 ) ( 1 000 001 + 2)
(1 000 000 - 4 )² - ( 1 000 000 - 1 ) ( 1 000 000 + 3 )
=1 000 000² - 8 000 000 + 16 - 1 000 000² - 3 000 000 + 1 000 000 + 3
Je te laisse continuer en espérant que tu réussisse.
0 votes
Thanks 1
helloevery
merci
Quantum
Verified answer
Bonjour
en utilisant les identités remarquables
soit x = 1 000 000
999 996 = 1 000 000 -4 = x -4
999 999 = 1 000 000 -1 =x-1
1 000 003 = 1 000 000 +3 = x+3
(x-4)² -(x-1)(x+3)
x²-8x+16 -(x²+3x-x-3)
x²-8x+16-x²-2x+3
-10x +19
-10( 1 000 000) +19 = - 10 000 000 +19 = - 9 999 981
0 votes
Thanks 1
helloevery
merci
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Lista de comentários
999 996² = ( 1 000 000 - 4 )²
999 999 × 1 000 003 = ( 1 000 001 - 2 ) ( 1 000 001 + 2)
(1 000 000 - 4 )² - ( 1 000 000 - 1 ) ( 1 000 000 + 3 )
=1 000 000² - 8 000 000 + 16 - 1 000 000² - 3 000 000 + 1 000 000 + 3
Je te laisse continuer en espérant que tu réussisse.
Verified answer
Bonjouren utilisant les identités remarquables
soit x = 1 000 000
999 996 = 1 000 000 -4 = x -4
999 999 = 1 000 000 -1 =x-1
1 000 003 = 1 000 000 +3 = x+3
(x-4)² -(x-1)(x+3)
x²-8x+16 -(x²+3x-x-3)
x²-8x+16-x²-2x+3
-10x +19
-10( 1 000 000) +19 = - 10 000 000 +19 = - 9 999 981