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free1973
@free1973
January 2021
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Bonjour, pouvez-vous m'aider s'il-vous-plaît?
Comment peut-on réduire, sans calculatrice, le résultat de 99 997²- 99 999 x 99 998 ?
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slyz007
Verified answer
Bonjour
Si on pose x=100000 l'expression équivaut à (x-3)²-(x-1)(x-2)
Or (x-3)²-(x-1)(x-2)=x²-6x+9-(x²-2x-x+2)=x²-6x+9-x²+3x-2=-3x+7
Donc 99997²-99999x99998=-3x100000+7=-300000+7=-299993
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Verified answer
BonjourSi on pose x=100000 l'expression équivaut à (x-3)²-(x-1)(x-2)
Or (x-3)²-(x-1)(x-2)=x²-6x+9-(x²-2x-x+2)=x²-6x+9-x²+3x-2=-3x+7
Donc 99997²-99999x99998=-3x100000+7=-300000+7=-299993