Réponses

2013-05-26T15:14:05+02:00

Exercice 13 :

 

1.

A = (2x - 1)² + (2x - 1) (-x-3)

A = (2x - 1) (2x - 1) + (2x - 1) (- x - 3)

A = (2x - 1) (2x - 1 - x - 3)

A = (2x - 1) (x - 4)

 

2.

A = (2x - 1) (x - 4)

A = 2x * x + 2x * (-4) - 1 * x - 1 * (-4)

A = 2x² - 8x - x - 4

A = 2x² - 9x - 4

Donc A = B

 

3.

B = 2x² - 9x - 4

B = 2 x (√5)² - 9 x (√5) - 4

B = 10 - 9√5 - 4

B = 6 - 9√5

 

4.

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

Soit :

(2x - 1) = 0

donc 2x - 1 = 0

2x = 1

x = 1/2

 

ou soit : (x - 4) = 0

donc x - 4 = 0

x = 4

 

S = {1/2 ; 4}