Bonsoir,
Développer :
(a + b)(c - d) = a x c + a x (-d) + b x c + b x (-d) = ac - ad + bc - bd
(2 - 3x)^2 = 2(2x - 1)(x + 1) - 5(3 - x)(4 + 7x)
4 - 12x + 9x^2 = (4x - 2)(x + 1) - (15 - 5x)(4 + 7x)
4 - 12x + 9x^2 = 4x^2 + 4x - 2x - 2 - (60 + 105x - 20x - 35x^2)
9x^2 - 12x + 4 = 4x^2 + 35x^2 + 2x - 85x - 2 - 60
9x^2 - 4x^2 - 12x + 83x + 4 + 62 = 0
5x^2 + 71x + 66 = 0
Tu calcules le discriminant :
Delta = 71^2 - 4 * 5 * 66)
Delta = 3721
Vdelta = 61 > 0 deux solutions
X1 = (-71 - 61) / (2 * 5)
X1 = -132/10
X1 = -66/5
X2 = (-71 + 61)/(2*5)
X2 = -10/10
X2 = (-1)
Factoriser :
a^2 - b^2 = (a - b)(a + b)
(a - b)^2 = a^2 - 2ab + b^2
ab + bc = b(a + c)
Voici comment on factorise.
a) 28x^2 - 49x = 0
(7 * 4 * x^2) - (7 * 7 * x) = 0
7x(4x - 7) = 0
Pour qu'un produit soit nul il faut qu'au moins l'un de ses facteurs soit nul :
7x = 0
x = 0
4x - 7 = 0
4x = 7
x = 7/4
S = {0;7/4}
b) 24x = 42x^2
42x^2 - 24x = 0
(6 * 7 * x^2) - (6 * 4 * x) = 0
6x(7x - 4) = 0
6x = 0
x = 0
Ou
7x - 4 = 0
7x = 4
x = 4/7
S = {0 ; 4/7}
c) 64x^2 - 48x + 9 =0
(8x)^2 - 2 * 8x * 3 + (3)^2 = 0
(8x - 3)^2 = 0
8x - 3 = 0
8x = 3
x = 3/8
S = {3/8}
d) 81 - 9x^2 = 0
9(9 - x^2) = 0
9(3^2 - x^2) = 0
9(3 - x)(3 + x) = 0
3 - x = 0
x = 3
Ou
3 + x = 0
x = (-3)
S = {-3;3}
e) la dernière je te laisse faire :)
