Réponse :
Explications étape par étape
Bonjour
Montrer que :
(x + 5)(x + 3) - 15 = x(x + 8)
x^2 + 3x + 5x + 15 - 15 = x(x + 8)
x^2 + 8x = x(x + 8)
x(x + 8) = x(x + 8)
En déduire les solutions de l’inéquation :
(x + 5)(x + 3) > 15
(x + 5)(x + 3) - 15 > 0
x(x + 8) > 0
x..........|-inf.............(-8)............0..............+inf
x..........|..........(-)...............(-)......||.....(+).........
x + 8...|.........(-)........||......(+)............(+).........
Ineq....|.........(+).......||......(-)......||.....(+).........
[tex]x \in ]-\infty ; -8[ U ]0 ; +\infty[[/tex]
Montrer :
(-2x + 1)(x - 3) + 25 = (-2x + 11)(x + 2)
-2x^2 + 6x + x - 3 + 25 = (-2x + 11)(x + 2)
-2x^2 + 7x + 22 = (-2x + 11)(x + 2)
-2x^2 + 7x + 22 = -2x^2 - 4x + 11x + 22
-2x^2 + 7x + 22 = -2x^2 + 7x + 22
En déduire Les solutions :
(-2x + 1)(x - 3) [tex]\ge[/tex] -25
(-2x + 1)(x - 3) + 25 [tex]\ge[/tex] 0
(-2x + 11)(x + 2) [tex]\ge[/tex] 0
-2x + 11 = 0 ou x + 2 = 0
2x = 11 ou x = -2
x = 11/2 ou x = -2
x.........|-inf...........(-2).............11/2...........+inf
-2x+11|.........(+).............(+)........o.......(-)......
x+2....|.........(-)......o......(+).................(+).....
Ineq...|.........(-).....o......(+)........o.......(-).......
[tex]x \in [-2 ; \dfrac{11}{2}][/tex]
Montrer :
7 + (-2x + 7)(x - 6) = (-x + 7)(2x - 5)
7 - 2x^2 + 12x + 7x - 42 = (-x + 7)(2x - 5)
-2x^2 + 19x - 35 = (-x + 7)(2x - 5)
-2x^2 + 19x - 35 = -2x^2 + 5x + 14x - 35
-2x^2 + 19x - 35 = -2x^2 + 19x - 35
En déduire les solutions :
(-2x + 7)(x - 6) < -7
(-2x + 7)(x - 6) + 7 < 0
(-x + 7)(2x - 5) < 0
-x + 7 = 0 ou 2x - 5 = 0
x = 7 ou 2x = 5
x = 7 ou x = 5/2
x............|-inf.............5/2.............7.............+inf
-x + 7....|..........(+)..............(+)......||.......(-)..........
2x - 5...|..........(-)........||......(+)...............(+)........
Ineq.....|...........(-).......||.......(+).....||.......(-).........
[tex]x \in ]-\infty ; \dfrac{5}{2}[ U ]7 ; +\infty[[/tex]
