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AM234
@AM234
May 2019
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Bonjour, je cherche à résoudre cet exercice mais je n'obtiens pas le résultat adéquat ; pouvez vous m aider svp :
Démontrer que la fonction f définie sur R par :
f(x) = (x-1)^3-(x+1)(x-1)²-(x-1)(1-2x)
Nous devons obtenir un résultat ax + b or j'obtiens que x
Merci d avance :)
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RomainVTT
F(x) = (x-1)³-(x+1)(x-1)²-(x-1)(1-2x)
= (x³ -3x² + 3x -1) - (x +1)(x² -2x+1) -(x -2x² -1 +2x)
= (x³ -3x² + 3x – 1) - (x³ -2x² +x -x² +2x +1) -(x -2x² -x +2x)
= x³ -3x² +3x -1 -x³ +2x² -x +x² -2x -1 -x +2x² +x -2x
= x³ -x³ -3x² +2x² +x² +2x² +3x -x -2x -x +x -2x -1 -1
= 2x² -2
= 2 (x² -1)
1 votes
Thanks 0
AM234
merci beaucoup !
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= (x³ -3x² + 3x -1) - (x +1)(x² -2x+1) -(x -2x² -1 +2x)
= (x³ -3x² + 3x – 1) - (x³ -2x² +x -x² +2x +1) -(x -2x² -x +2x)
= x³ -3x² +3x -1 -x³ +2x² -x +x² -2x -1 -x +2x² +x -2x
= x³ -x³ -3x² +2x² +x² +2x² +3x -x -2x -x +x -2x -1 -1
= 2x² -2
= 2 (x² -1)