Bonjour , j'aurai besoin d'aide pour un exercice :
Résoudre les inéquations suivantes
1) (3x+5) (3x-5) - 2 (3x-5) ² ≤ 0
2) (8x+1) (-3x+4) (6x+7) ≥ 0
3) (2x-3) ² > (3x+7) ²
4) x ³ < 25 x
Bonjour,
1) (3x+5) (3x-5) - 2 (3x-5) ² ≤ 0
(3x-5)(3x+5 - 2 (3x-5)) ≤ 0
(3x-5)(3x+5 - 6x+10) ≤ 0
(3x-5)(-3x+15) ≤ 0
A = 3(3x-5)(-x+5) ≤ 0
x1 = 5/3 et x2 = 5
x -inf 5/3 5 +inf
(3x-5) - 0 + +
(-x+5) + + 0 -
A - 0 + 0 -
S= ] -inf ; 5/3 ] U [ 5 ; +inf [
2) B = (8x+1) (-3x+4) (6x+7) ≥ 0
x1 = -1/8 ; x2 = 4/3 ; x3 = -7/6
x -inf -7/6 -1/8 4/3 +inf
(8x+1) - - 0 + +
(-3x+4) + + + 0 -
(6x+7) - 0 + + +
B + 0 - 0 + 0 -
S= ] -inf ; -7/6 ] U [ -1/8 ; 4/3 ]
3) (2x-3) ² > (3x+7) ²
(2x-3) ² - (3x+7) ² > 0
4x²-12x+9-(9x²+42x+49 > 0
4x²-12x+9-9x²-42x-49 > 0
-5x²-54x-40 > 0
C = 5x²+54x+40 < 0
delta = 54²-(4*5*40) = 2116 = 46²
x1 =( -54+46)/10 = -8/10 = -4/5
x2 = ( -54-46)/10 = -100/10 = -10
C < 0
S= ] -10 ; -4/5[
4) x ³ < 25 x
x ³-25x < 0
x(x²-25) < 0
D = x(x+5)(x-5) < 0
x -inf -5 0 5 +inf
x - - 0 + +
(x+5) - 0 + + +
(x-5) + + + 0 -
D + 0 - 0 + 0 -
D < 0
S = ]-5 ; 0 [ U ]-5 ; 0 [5 ; +inf [
J'espère que tu as compris
a+