Réponse :
Explications étape par étape
Bonjour
Résoudre :
9x^2 - 5x + 1 = 4x - 3
9x^2 - 5x - 4x + 1 + 3 = 0
9x^2 - 9x + 4 = 0
(3x)^2 - 2 * 3x * 3/2 + (3/2)^2 - (3/2)^2 + 4 = 0
(3x - 3/2)^2 - 9/4 + 16/4 = 0
(3x - 3/2)^2 = -7/4
Un carré est toujours positif donc pas de solution
(2x - 7)(6x^2 - 5x + 1) >> 0
2x - 7 = 0 et 6x^2 - 5x + 1 = 0
2x = 7 et [tex]\Delta = (-5)^{2} - 4 * 6 * 1 = 25 - 24 = 1[/tex]
x = 7/2 et x1 = (5 - 1)/(2 * 6) et x2 = (5 + 1)/(2 * 6)
x = 7/2 et x1 = 4/12 et x2 = 6/12
x = 7/2 et x1 = 1/3 et x2 = 1/2
x.........|-inf..........1/3........1/2........7/2........+inf
2x-7...|.......(-)............(-)..........(-).....o...(+).........
6x^2...|......(+).....o....(-)....o....(+).........(+).........
Ineq....|......(-)......o....(+)...o....(-)....o...(+)........
[tex]x \in [1/3 ; 1/2] U [7/2 ; +\infty[[/tex]
(7x^2 - 9x + 3)/(-2x - 1) < -7
-2x - 1 # 0
2x # -1
x # -1/2
7x^2 - 9x + 3 < -7(-2x - 1)
7x^2 - 9x + 3 < 14x + 7
7x^2 - 9x - 14x + 3 - 7 < 0
7x^2 - 23x - 4 < 0
[tex]\Delta = (-23)^{2} - 4 * 7 * (-4) = 529 + 112 = 641[/tex]
[tex]\sqrt{\Delta} \approx 25,31[/tex]
X1 = (23 - 25,31)/(2 * 7) = -0,165
X2 = (23 + 25,31)/14 = 3,45
x............|-inf..........x1...........x2..........+inf
7x^2.....|........(+)....o....(-)......o.....(+)........
[tex]x \in ]x1 ; x2[[/tex]
