Réponse :
Explications étape par étape
Bonsoir
A(x) = (x - 2 * 60)(x - 30)
b) developper :
A(x) = (x - 120)(x - 30)
A(x) = x^2 - 30x - 120x + 3600
A(x) = x^2 - 150x + 3600
c) developper :
(x - 75)^2 - 2025 = x^2 - 150x + 5625 - 2025 = x^2 - 150x + 3600
2) a) 1000 < (x - 75)^2 - 2025 < 2200
b) (x - 75)^2 - 2025 > 1000
(x - 75)^2 - 2025 - 1000 > 0
(x - 75)^2 - 3025 > 0
(x - 75 - 55)(x - 75 + 55) > 0
(x - 130)(x - 20) > 0
(x - 75)^2 - 2025 < 2200
(x - 75)^2 - 2025 - 2200 < 0
(x - 75)^2 - 4225 < 0
(x - 75 - 65)(x - 75 + 65) < 0
(x - 140)(x - 10) < 0
c) tableau :
x - 130 = 0 et x - 20 = 0
x = 130 et x = 20
x...........|-inf.................20...............130..........+inf
x-130....|............(-).................(-).........o.......(+).......
x-20.....|.............(-)........o......(+)..................(+).......
Ineq.....|..............(+).......o.......(-)........o.......(+).........
[tex]x \in ]-\infty ; 20] U [130 ; +\infty [[/tex]
x - 140 = 0 et x - 10 = 0
x = 140 et x = 10
x...........|-inf.................10...............140..........+inf
x-140....|............(-).................(-).........o.......(+).......
x-10.....|.............(-)........o......(+)..................(+).......
Ineq.....|..............(+).......o.......(-)........o.......(+).........
[tex]x \in [10 ; 140][/tex]
