Réponses

2013-03-31T21:29:41+02:00

3.1) 81x² - 16 = (9x)² - 4² = (9x - 4)(9x + 4)

(2x - 1)(9x + 4) + 81x² = 16

(2x - 1)(9x + 4) + 81x² - 16 = 0

(2x - 1)(9x + 4) + (9x + 4)(9x - 4) = 0

(9x + 4)[(2x - 1) + (9x - 4) = 0

(9x + 4)(11x - 5) = 0

x = -4/5 ou x = 5/11.

 

2) 9x² - 24x + 16 = (3x - 4)²

9x² = 24x - 16

9x² - 24x + 16 = 0

(3x - 4)² = 0

x = 4/3

 

4.1) 9(x + 3)² = 25

9(x + 3)² - 25 = 0

(3(x + 3) - 25)(3(x + 3) + 25) = 0

(3x - 16)(3x + 34) = 0

x = 16/3 ou x = -34/4 = -17/2

 

2) (3x + 1)² - (x + 2)(4x - 1) = 5(x - 1)²

(9x² + 6x + 1) - (4x² + 7x - 2) = 5x² - 10x + 5.

5x² - x + 3 = 5x² - 10x + 5

9x = 2

x = 2/9