Réponse :
a.
x² = 9
x² - 9 = 0
(x + 3)(x - 3) = 0 [Identité remarquable]
x+3 = 0 ou x-3 = 0
S = {-3 ; 3}
b.
x² = 13
(x - 13/2)(x + 13/2) = 0
x - 13/2 = 0 ou x + 13/2 = 0
S = {-13/2 ; 13/2}
c.
3(x - 5) = 3x(x - 5)
3(x - 5) - 3x(x - 5) = 0
(x - 5)(3 - 3x) = 0 [on factorise par x-5]
x - 5 = 0 ou 3 - 3x = 0
S = {1 ; 5}
d.
4(2x - 4) = -3x(2x - 4)
4(2x - 4) + 3x(2x - 4) = 0
(2x - 4)(4 + 3x) = 0
2x - 4 = 0 ou 4 + 3x = 0
S = {-3/4 ; 2}
e.
(2x + 1)(3x - 7) = (2x + 1)(x + 5)
(2x+1)(3x - 7 - x - 5) = 0
(2x+1)(2x - 12) = 0
2x + 1 = 0 ou 2x - 12 = 0
S = {-1/2 ; 6}
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Réponse :
a.
x² = 9
x² - 9 = 0
(x + 3)(x - 3) = 0 [Identité remarquable]
x+3 = 0 ou x-3 = 0
S = {-3 ; 3}
b.
x² = 13
(x - 13/2)(x + 13/2) = 0
x - 13/2 = 0 ou x + 13/2 = 0
S = {-13/2 ; 13/2}
c.
3(x - 5) = 3x(x - 5)
3(x - 5) - 3x(x - 5) = 0
(x - 5)(3 - 3x) = 0 [on factorise par x-5]
x - 5 = 0 ou 3 - 3x = 0
S = {1 ; 5}
d.
4(2x - 4) = -3x(2x - 4)
4(2x - 4) + 3x(2x - 4) = 0
(2x - 4)(4 + 3x) = 0
2x - 4 = 0 ou 4 + 3x = 0
S = {-3/4 ; 2}
e.
(2x + 1)(3x - 7) = (2x + 1)(x + 5)
(2x+1)(3x - 7 - x - 5) = 0
(2x+1)(2x - 12) = 0
2x + 1 = 0 ou 2x - 12 = 0
S = {-1/2 ; 6}