Sagot :
Réponse :
E(x) = 12x² - 3 - (x-2)(2x-1)
F(x) = (2x-1)(3x+2)
1) 12x² - 3 = 3(2x-1)(2x+1)
12x² - 3 = 3(4x² + 2x - 2x - 1)
12x² - 3 = 3(4x² - 1)
12x² - 3 = 12x² - 3
2) E(x) = 12x² - 3 - (x - 2)(2x - 1) = 3(2x - 1)(2x + 1) - (x - 2)(2x - 1) = (2x - 1) [3(2x + 1) - (x - 2)]
3) E(x) = (2x - 1) [3(2x + 1) - (x - 2)] = 0
(2x - 1) (6x + 3 - x + 2) = 0
(2x - 1)(5x + 5) = 0
10x² + 10x - 5x - 5 = 0
10x² + 5x - 5 = 0
4) F(x) = (2x - 1)(3x + 2) = 6x² + 4x - 3x - 2 = 6x² + x - 2
5) P(x) = F(x)
a) (2x - 1)(3x + 2) = 0
*2x - 1 = 0 2x = 1 x = 1/2
*3x + 2 = 0 3x = -2 x = -2/3
b) P(x) = 15
(2x - 1)(3x + 2) = 15
*2x - 1 = 15 2x = 15 + 1 = 16 x = 16/2 = 8
*3x + 2 = 15 3x = 15 - 2 = 13 x = 13/3
c) P(x) = 7
*(2x - 1) = 7 2x = 7 + 1 = 8 x = 8/2 = 4
*3x + 2 = 7 3x = 7 - 2 = 5 x = 5/3
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