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Chichkebabman
@Chichkebabman
April 2019
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On donne l'expression suivante : E = 81 - ( 2x - 5 )² + 4 ( 4 + 2x )
1/ Developper : E
2/ Factoriser: 81 - ( 2x - 5 )²
3/ En deduire une factorisation de E
4/ Resoudre l'equation E = 0
svp aidez moi c'est pour demain et en plus il faut mettre tout les calculs
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Commentaires (2)
Bonsoir,
E = 81 - ( 2x - 5 )² + 4 ( 4 + 2x )
1/ Développer :
E
E = 81 - ( 4x² - 20x + 25) + (16 + 8x)
E = 81 - 4x² + 20x - 25 + 16 + 8x
E = -4x² + 28x + 56
2/ Factoriser: 81 - ( 2x - 5 )²
81 - ( 2x - 5 )² = 9² - (2x - 5)²
= [9 + (2x - 5)][9 - (2x - 5)]
= (9 + 2x - 5)(9 - 2x + 5)
= (4 + 2x)(14 - 2x)
3/ En deduire une factorisation de E
E = 81 - ( 2x - 5 )² + 4 ( 4 + 2x )
E = (4 + 2x)(14 - 2x) + 4(4 + 2x)
E =(4 + 2x)[(14 - 2x) + 4]
E =(4 + 2x)(14 - 2x + 4)
E =(4 + 2x)(18 - 2x)
4/ Resoudre l'equation E = 0
(4 + 2x)(18 - 2x) = 0
4 + 2x = 0 ou 18 - 2x = 0
2x = -4 ou -2x = -18
x = -4/2 ou x = (-18)/(-2)
x = -2 ou x = 9.
S = {-2 ; 9}
1 votes
Thanks 1
chichkebabman
merci beaucoup tu me sauve la vie
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E = 81 - ( 2x - 5 )² + 4 ( 4 + 2x )
1/ Développer : E
E = 81 - ( 4x² - 20x + 25) + (16 + 8x)
E = 81 - 4x² + 20x - 25 + 16 + 8x
E = -4x² + 28x + 56
2/ Factoriser: 81 - ( 2x - 5 )²
81 - ( 2x - 5 )² = 9² - (2x - 5)²
= [9 + (2x - 5)][9 - (2x - 5)]
= (9 + 2x - 5)(9 - 2x + 5)
= (4 + 2x)(14 - 2x)
3/ En deduire une factorisation de E
E = 81 - ( 2x - 5 )² + 4 ( 4 + 2x )
E = (4 + 2x)(14 - 2x) + 4(4 + 2x)
E =(4 + 2x)[(14 - 2x) + 4]
E =(4 + 2x)(14 - 2x + 4)
E =(4 + 2x)(18 - 2x)
4/ Resoudre l'equation E = 0
(4 + 2x)(18 - 2x) = 0
4 + 2x = 0 ou 18 - 2x = 0
2x = -4 ou -2x = -18
x = -4/2 ou x = (-18)/(-2)
x = -2 ou x = 9.
S = {-2 ; 9}