[[Mathematiques]] Savoir Faire 5 A(a) = (x+3)P2 - 25 1) D = A(x) = (x+3)P2 - 25 (x+3)(x+3) - 25 x P2 + 6x + 9 - 25 x^2 + 6x - 16 F = A(x) = (8+x)(-2+x) 2) A(0) = (8 + x) (-2 + x) **(8+0) (-2+0)** -16 3) A(-3) (8-3)(-2 - 3) -16 - 24 + 6 + 9 -25 4) A (-8) (8-8)(-2-8) -16 - 64 + 16 + 64 0 **Savoir faire n°6** 1) 4x-4 = 5-3x-2+x-1 6x = 6 x =1 2) (2x+4)(9x-3)=0 18x-6x+36x-12=0 x = -2 ou x = 3 3) (x+3) P de 2 - 25 = 0 *Factoriser* x P de 2 + 6x +9 -25 = 0 x P de 2 + 6x -16 = 0 4) (x + 5) / (x-2) - 3 = 0 Exercice 5 fiche exercice : F = (x-9)^2 = x^2 - 18x + 81 =**juste** G = (3x + 5)^2 - (x - 5) G = 9x^2 + 30x + 25 - x + 5 G = 9x^2+ 29x + 30 = **juste** H = (x + 4)(x - 4) - 3 H = x^2 - 8x + 16 - 3 H = x^2 - 8x + 13 = **faux** I = ((x + 1)(x-2)) (x+3) I = (x^2 - 1x - 2) (x+3) I = x^3 + 2x^2 - 5x - 6 Exercice 6 fiche exercice J = 4(x-3) + x(x-3) J = 4x - 12 + X^2 - 3x J = x^2 + 1x - 12 K = (x+2)^2 - 36 K = x^2 + 4x + 4 - 36 K = x^2 + 4x - 32 L = 4x^2 - 20x + 25 Factoriser (x+3+5) (x+3-5) 1) B(x) - A(x) = 1000 - 5x - (45 + 5x) = 1000 - 5x - 45 - 5x = 955 - 10x = 955 - 10x < 0 = 955 < 10x 955/10 > x 95.5 > x donc B(x) > A(x) lorsque x < 95.5 2) C/D = n^5/5 // n^4/ 4 = n^5/5 x 4/n^4 = 4/5 x n^5/n^4 = 4/5 x n = 0.8 x N > 1 car n > 2 Donc C>D Exemple Exercice 1 a < b 7a - 5 ... ?.... 7b - 5 a x 7 b x 7 7a < 7b 7a - 5< 7b - 5 Exercice 2 a ≥ b 3 - 4a ..?.. 3 - 4b a x -4 ≥ b x -4 - 4a ≥ - 4b donc - 4a + 3 ≥ - 4b + 5 Exercice 3 a ≤ 3 et b ≤ -2 5 x a ≤ 3 x 5 et b x 2 ≤ -2 x 2 5a ≤ 15 et 2b ≤ - 4 Donc 5a + 2b ≤ 15 - 4 5a + 2b ≤ 11 Exercice 4 a ≤ 2 et ≤ 3 a x -3 ≤ 2 x - 3 b x 5 ≤ 3 x 5 -3a ≤ -6 5b ≤ 15 -3a + 5b ≤ -9 + 15 -3a + 5b ≤ 9 Exemple 2 1) 7x - 4 > 0 7x ≥ 4 x ≥ 4/7 **==Solution {4/7 ; + oo}==** 2) x - 6 > 4x + 3 -3x > 9 9/-3 < x -3 < x **==Solution {-oo ; -3}==** 3) 7x - 4 < 2x + 1 5 5x < 5 x 5 5x 25 x < 5 **==Solution {5;+oo}==** A(x) = x(3x + 1) – (2x + 5) (3x + 1) A(x) = 3x² + x – 6x² + 2x + 15x + 5 A(x) = -3x² + 18x + 5 (3x + 1) (3x + 5) Si x = 0 alors A(x) = + 5 20 a et b p47 x(2x + 7)(x + 2) = 0 x = 0 5x² + 8x = 0 x = 0 21 a p47 3x + 2 / x² + 4 = 0 3x + 2 = 0 et x² + 4 ≠ 0 135 p 55 3x + 4 < x + 2 3x ≤ x