Réponse :
Explications étape par étape
a/ (x + 3) (x + 2) + x² + 4x + 4 = 0
⇔ (x + 3) (x + 2) + (x + 2)² = 0
⇔ ( x + 3) (x + 2) + ( x +2 ) ( x +2 ) = 0
⇔ (x + 2) [ ( x + 3) +( x +2 ) ] = 0
⇔ ( x + 2 ) ( 2x + 5 ) = 0
x+2 = 0 ou 2x + 5 = 0
⇔ x = -2 ⇔ 2x = -5
⇔ x = -5/2
S = { -5/2 ; -2 }
b/ x² + 6x + 9 = x (x – 4)
⇔ x² + 6x + 9 = x² - 4x
⇔ 10x + 9 = 0
⇔ 10x = -9
⇔ x = -9 /10
c/ (2x - 1) (x + 5) = 4x² – 1
⇔ 2x² + 10 x - x - 5
⇔ 2x² + 9x - 5 = 4x² - 1
⇔ 2x² + 9x - 4 = 4x²
⇔ -2x² + 9x - 4 = 0
Δ = b²- 4ac = 9²- 4 · (-2)·(-4) = 81 - 32 = 49
Δ>0
x₁ = 4
x₂ = 0,5
