Réponses

2013-05-10T19:03:21+02:00

Exo 01:


1. x² > 9
    x² - 9 > 0
    (x-3)(x+3) > 0
    x > 3 ou x < 3

 

2. (2x-3)/(x-3) - 1 < 0
    (2x-3 - x+3)/(x-3) < 0
     x/(x-3) < 0
     x > 0 et x-3 < 0
     0 < x < 3

 

3. 3x(x - 3) < 0
    0 < x < 3

 

Exo 02:
(2-2x)(1-x) = 2(1-x)² > 0.5
(1 - x)² > 0.25
(1-x)² - 0.25 > 0
(1 - x - 0.5)(1 - x + 0.5) > 0
(0.5 - x)(1.5 - x) > 0
x < 0.5 ou x > 1.5
or on a 0 < x < 1
donc 0 < x < 0.5