Réponse :
Explications étape par étape
56 a/ ( x + 8 ) ( x - 5 ) = 0
Il suffit que l'un des membres du produit soit nul.
x + 8 = 0
⇔ x = -8
x - 5 = 0
⇔ x = 5
S = { -8, 5 }
b/ 5x( 4 - x ) = 0
5x = 0
⇔ x = 0
4 - x = 0
⇔ x = 4
S = { 0 , 4 }
c/ ( x + 3 )² = 0
x + 3 = 0
⇔ x = -3
S = { -3 }
57/a ( 2x + 7 ) (3 x - 12 ) = 0
2x + 7 = 0
⇔ 2x = -7
⇔ x = -7/2
3x -12 = 0
⇔ 3x = 12
⇔ x = 4
S = { -7/2 , 4 }
b/ (5y - 2 ) ( 6y + 9 ) = 0
5y -2 = 0
⇔ 5y = 2
⇔ y = 2/5
6y + 9 = 0
⇔ 6y = -9
⇔ y = -9/6 = -3/2
S = { -3/2 , 2/5 }
58/ 2x (4x - 5 ) = 0
2x = 0
⇔ x = 0
4x - 5 = 0
⇔ 4x = 5
⇔ x =5/4
S = { 0, 5/4 }
b/ ( 3 - 2n ) ( n + 4 ) = 0
⇔ 3 - 2n = 0
⇔ - 2n = -3
⇔ 2n = 3
⇔ n = 3/2
n + 4 = 0
⇔ n = -4
S = { -4, 3/2 }
59/a ( 2x + 1 ) ( 3x - 5 ) = 0
2x +1 = 0
⇔ 2x = -1
⇔ x = -1/2
3x - 5 = 0
⇔ 3x = 5
⇔ x = 5/3
S = { -1/2 , 5/3 }
Ce sont des nombres rationnels, quotient de deux entiers relatifs.
2 ( 4y - 3 ) ( 6y + 1 ) = 0
4y - 3 = 0
⇔ 4y = 3
⇔ y = 3/4
6y + 1 = 0
⇔ 6y = -1
⇔ y = -1/6
S = {-1/6 , 3/4 }
Ce sont des nombres rationnels, quotient de deux entiers relatifs.
60/ x² - 5x = 0
⇔ x ( x -5 ) = 0
S = {0 , 5}
6x² - 18x = 0
⇔ 6x ( x -3 ) = 0
S = { 0, 3}
61/ x² - 4 = 0
(x - 2 ) ( x + 2 ) = 0
S = { -2, 2 }
x² - 6x + 9 = 0
⇔ x² - 3x - 3x + 9 = 0
⇔ x ( x -3 ) - 3 ( x - 3 ) = 0
⇔ (x - 3 ) (x - 3) = 0
S = { 3}
