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elsa170
@elsa170
June 2021
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Exercice 2 et exercice 3 SVP je ne comprend pas merci d'avance
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senmusa
Exercice 2
E=(16 - 25 x²) - 3(4 - 5x)(3x + 9)
1) développer et réduire:
E = 16 - 25x² -3(12x + 36 - 15x² - 45x)
= 16 - 25x² -3( -15x² -33x +36)
= 16 - 25x² + 45x² + 99x - 108
= 20x² + 99x - 92
2)a) x=0
E = - 92
b) x= -1/2
E= 20(1/4) - 99/2 - 92
= 10/2 - 99/2 - 184/2 = -273/2
c) x= -3
E = 20(9) + 99(-3) - 92
= 180 - 297 - 92 = -209
3) F = 16 - 25x²
différence de deux carrés
F = (4 - 5x)(4 + 5x)
4) factorisation de E
E =(4 - 5x)(4 + 5x) - 3(4 - 5x)(3x + 9)
= (4-5x) ( 4+5x -9x - 27)
= (4-5x) (-4x - 23)
= - (4-5x)(23+4x)
5) E = 0
==> 4-5x=0 <==> x = 4/5 ou 23+4x=0 <==> x = -23/4
===> S = { -23/4 ; 4/5}
Exercice 3
Vrai ou faux
(n+1)² - (n-1)² = ( n+1 + n - 1)(n+1 -n +1) = 2n(2)=4n
===> l'affirmation est vraie quel que soit n
1 votes
Thanks 1
elsa170
merci beaucoup mais la justification de la 3?!
senmusa
quel que soit n si tu le multiplie par 4 (puisque 4n) c'est un multiple de 4
senmusa
et de rien
elsa170
merci vraiment beaucoup :)
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E=(16 - 25 x²) - 3(4 - 5x)(3x + 9)
1) développer et réduire:
E = 16 - 25x² -3(12x + 36 - 15x² - 45x)
= 16 - 25x² -3( -15x² -33x +36)
= 16 - 25x² + 45x² + 99x - 108
= 20x² + 99x - 92
2)a) x=0
E = - 92
b) x= -1/2
E= 20(1/4) - 99/2 - 92
= 10/2 - 99/2 - 184/2 = -273/2
c) x= -3
E = 20(9) + 99(-3) - 92
= 180 - 297 - 92 = -209
3) F = 16 - 25x²
différence de deux carrés
F = (4 - 5x)(4 + 5x)
4) factorisation de E
E =(4 - 5x)(4 + 5x) - 3(4 - 5x)(3x + 9)
= (4-5x) ( 4+5x -9x - 27)
= (4-5x) (-4x - 23)
= - (4-5x)(23+4x)
5) E = 0
==> 4-5x=0 <==> x = 4/5 ou 23+4x=0 <==> x = -23/4
===> S = { -23/4 ; 4/5}
Exercice 3
Vrai ou faux
(n+1)² - (n-1)² = ( n+1 + n - 1)(n+1 -n +1) = 2n(2)=4n
===> l'affirmation est vraie quel que soit n