Réponse :

Explications étape par étape

Bonjour

1.résoudre (2x-3)² ≥ (2x-3) (x+1)

(2x - 3)² - (2x - 3)(x + 1) ≥ 0

(2x - 3)(2x - 3 - x - 1) ≥ 0

(2x - 3)(x - 4) ≥ 0

2x - 3 = 0

2x = 3

x = 3/2

x - 4 = 0

x = 4

x............|-inf.............(3/2)............4.............+inf

2x-3......|..........(-)........o.......(+)..........(+)...........

x-4........|...........(-)..................(-).....o.....(+).........

Ineq.....|............(+).......o........(-).....o......(+).......

x € ]-inf ; 3/2] U [4;+inf [

2. résoudre (x-√3)(x-√5) ≤ 0

x.............|-inf...............√3............√5............+inf

x-√3......|..........(-).........o.....(+).............(+)...........

x-√5......|...........(-)................(-).......o.....(+)..........

Ineq.......|...........(+).......o......(-)......o......(+)........

x € [√3 ; √5]

3. résoudre (x-4)² ≤ x²-16

(x - 4)² ≤ (x - 4)(x + 4)

(x - 4)² - (x - 4)(x + 4) ≤ 0

(x - 4)(x - 4 - x - 4) ≤ 0

(x - 4)(-8) ≤ 0

-8(x - 4) ≤ 0

-8x + 32 ≤ 0

32 ≤ 8x

32/8 ≤ x

4 ≤ x

x € [4 ; +inf [