1) 3x² - 14x + 8 = 0 => 3(x² - 14/3x + 8/3) = 0 => x² - 14/3x + 49/9 -25/9 = 0
x² - 14/3x + 49/9 -25/9 = 0 =>( x² - 14/3x + 49/9) -25/9 = 0 => (x-7/3)² = 25/9
x - 7/3 = 5/3 => x = 12/3 = 4
x - 7/3 =- 5/3 => x = 2/3
2)x²+25 = 10x => x² - 10 + 25 = 0 => (x-5)² = 0 => x = 5
3) 5x-3/x-2 = 0 => il faut x différent de 2
(5x(x-2) - 3) = 0 => 5x² - 10x - 3 = 0 => 5(x² - 2x -3/5) = 0
=> x² - 2x + 1 -8/5 = 0 => (x-1)² = 8/5 et tu continues comme au 1)
4) attention il aut x dif de -1 et -3
produit en croix
x+3 = 3x + 3 => 2x = 0 => x = 0
Exercice 2
1) (x+2)(X-5) <ou= 0 tableau de signes
x -2 5
+ 0 - 0 + solution [-2;5]
2) 7(-x-1/2)(2/3x-4) <ou= 0
x -1/2 6
- 0 + 0 - solution <--- ; -1/2] U [6;--->
3) x(-5x+4) > 0
x 0 4/5
- 0 + 0 - solution ]0;4/5[
4) (x+3)² >ou= 16 => (x+3)²- 16 >=0 => (x+3+4)(x+3-4) >= 0 (x+7)(x-1) >=0
x -7 1
+ 0 - 0 + solution <---;-7] U [1; --->
5) -3x+6/x-1 >ou= 0 x 1 2
- | + 0 - solution ]1;2]
6) 2x-5 > 4/2x-5 => 2x-5 - 4/2x-5 > 0 => ((2x-5)² - 4)/(2x-5) > 0 => (2x-5-2)(2x-5+2)/(2x-5) > 0
(2x-7)(2x-3)/(2x-5)
x 3/2 5/2 7/2
(2x-7) - - - 0 +
(2x-3) - 0 + + +
(2x-5) - - 0 + +
- 0 + | - 0 + solution ]3/2; 5/2[ U ]7/2; --->
