Réponse :
bonjour
a) 25x2 - (x + 1)2 = 0
( 5 x + x + 1 ) ( 5 x - x - 1 ) = 0
( 6 x + 1 ) ( 4 x - 1 ) = 0
⇔ x = - 1/6 ou 1/4
b) (3x - 1)(x + 1) = 3x2 + 4
3 x² + 3 x - x - 1 = 3 x² + 4
3 x² - 3 x² + 2 x = 4 + 1
2 x = 5
x = 5 /2
c) (x + 2)2 - 4x2 = 0
même chose que a = différence de 2 carrés
d) (2x - 1)2 = 4x(x + 2)
4 x² - 4 x + 1 = 4 x² + 8 x
4 x² - 4 x² - 4 x - 8 x = - 1
- 12 x = - 1
x = 1 /12
e) 3(2 - x) + 2x2 - 5 = x + 2(x + 3)2.
6 - 3 x + 2 x² - 5 = x + 2 ( x² + 6 x + 9 )
2 x² - 3 x + 1 = x + 2 x² + 12 x + 18
2 x² - 2 x² - 3 x - x - 12 x = 18 - 1
- 16 x = 17
x = - 17/16
f) (2x + 1)x2 - 4(2x + 1) = 0
( 2 x + 1 ) ( 2 x + 1 - 4 ) = 0
( 2 x + 1 ) ( 2 x - 3 ) = 0
⇔ x = - 1/2 ou 3 /2
