1) A(x) = (2x-4)(3-2x)
= 2x*3 + 2x*(-2x) + (-4)*3 + (-4)*(-2x)
= 6x - 2x² - 12 + 8x
= -2x² + 14x - 12
B(x) = -3(2x+5)²-x(5x-7)
= -3[2x² + 2*2x*5 + 5²] - [5x² - 7x]
= -3[2x² + 20x + 25] - 5x² + 7x
= -6x² - 60x - 75 - 5x² + 7x
= -11x² - 53x - 75
2) A(-2) = -2*(-2)² + 14*(-2) - 12
= -2*4 -28 - 12
= -8 - 40
= -48
B( = -11*()² - 53*() - 75
= -11* - - 75
= - - - 75
= - - -
= -
3) C(x) = (3x-1)(3-7x) - (3x-1)(8x+2)
= (3x-1)[(3-7x) - (8x+2)]
D(x) = (2x+1)² - 64
= (2x+1)² - 8²
4) C(x) = 0
(3x-1)[(3-7x) - (8x+2)] = 0
⇔ (3x-1)(3-7x) - (3x-1)(8x+2) = 0
⇔ 9x - 21x² - 3 + 7x - 24x² + 6x - 8x - 2 = 0
⇔ -45x² + 14x - 5 = 0
Pour résoudre cette équation, on doit calculer le discriminant Δ.
Δ = b² - 4ac
= 14² - (4*(-45)*(-5)
= 196 - 900
= -704 < Δ donc pas de solution réelle
D(x) = 64
(2x+1)² - 8² = 64
⇔ (2x+1)² - 64 = 64
⇔ (2x+1)² - 64 - 64 = 0
⇔ (2x+1)² - 128 = 0
⇔ [2x² + 2*2x*1 + 1²] - 128 = 0
⇔ 2x² + 4x + 1 - 128 = 0
⇔ 2x² + 4x -127 = 0
= 4² - (4*2*(-127))
= 16 + 1016
= 1032 > 0 donc 2 solutions distinctes.
x = = = -
y = = = -
J'espère t'avoir aidé.
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Lista de comentários
1) A(x) = (2x-4)(3-2x)
= 2x*3 + 2x*(-2x) + (-4)*3 + (-4)*(-2x)
= 6x - 2x² - 12 + 8x
= -2x² + 14x - 12
B(x) = -3(2x+5)²-x(5x-7)
= -3[2x² + 2*2x*5 + 5²] - [5x² - 7x]
= -3[2x² + 20x + 25] - 5x² + 7x
= -6x² - 60x - 75 - 5x² + 7x
= -11x² - 53x - 75
2) A(-2) = -2*(-2)² + 14*(-2) - 12
= -2*4 -28 - 12
= -8 - 40
= -48
B( = -11*()² - 53*() - 75
= -11* - - 75
= - - - 75
= - - -
= - - -
= -
3) C(x) = (3x-1)(3-7x) - (3x-1)(8x+2)
= (3x-1)[(3-7x) - (8x+2)]
D(x) = (2x+1)² - 64
= (2x+1)² - 8²
4) C(x) = 0
(3x-1)[(3-7x) - (8x+2)] = 0
⇔ (3x-1)(3-7x) - (3x-1)(8x+2) = 0
⇔ 9x - 21x² - 3 + 7x - 24x² + 6x - 8x - 2 = 0
⇔ -45x² + 14x - 5 = 0
Pour résoudre cette équation, on doit calculer le discriminant Δ.
Δ = b² - 4ac
= 14² - (4*(-45)*(-5)
= 196 - 900
= -704 < Δ donc pas de solution réelle
D(x) = 64
(2x+1)² - 8² = 64
⇔ (2x+1)² - 64 = 64
⇔ (2x+1)² - 64 - 64 = 0
⇔ (2x+1)² - 128 = 0
⇔ [2x² + 2*2x*1 + 1²] - 128 = 0
⇔ 2x² + 4x + 1 - 128 = 0
⇔ 2x² + 4x -127 = 0
Pour résoudre cette équation, on doit calculer le discriminant Δ.
Δ = b² - 4ac
= 4² - (4*2*(-127))
= 16 + 1016
= 1032 > 0 donc 2 solutions distinctes.
x = = = -
y = = = -
J'espère t'avoir aidé.