A(x) = (x - 3) (5 - x) +2x² -18 B(x) = (x + 11)(1-x) C(x) = (x+7)(x-3) 1) Développer a(x); B(x) et C(x) 2) En déduire les solutions des équations: A(x) =C(x) et
Mathématiques
fawes1
Question
A(x) = (x - 3) (5 - x) +2x² -18
B(x) = (x + 11)(1-x)
C(x) = (x+7)(x-3)
1) Développer a(x); B(x) et C(x)
2) En déduire les solutions des équations: A(x) =C(x) et A(x) = B(x) = 0
3) Factoriser A(x)
B(x) = (x + 11)(1-x)
C(x) = (x+7)(x-3)
1) Développer a(x); B(x) et C(x)
2) En déduire les solutions des équations: A(x) =C(x) et A(x) = B(x) = 0
3) Factoriser A(x)
1 Réponse
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1. Réponse danielwenin
1) A(x) = (x - 3) (5 - x) +2x² -18 = -x² - 3x + 5x - 15 + 2x² - 18 = x² + 2x - 33
B(x) = (x + 11)(1-x) = -x² + x + 11 - 11x = -x² - 10x + 11
C(x) = (x+7)(x-3) = x² + 7x - 3x - 21 = x² + 4x - 21
2) A(x) = C(x) => x² + 2x - 33 = x² + 4x - 21 => -2x = 12 => x = -6
A(x) = B(x) => x² + 2x - 33 = -x² - 10x + 11 => 2x² + 12x - 44 = 0 => x² + 6x - 22 = 0
=> (x² + 6x + 9 ) - 31 = 0 => (x+3)² - 31 = 0 => (x+3)² = 31 => x+3 = V31 => x= -3 + V31
=> x+3 = -V31 => x = -3 - V31
3)A(x) = (x - 3) (5 - x) + 2(x-3)(x+3) = (x-3)(5-x + 2x+6) = (x-3)(x+11)