Réponse :

Explications étape par étape

56 a/  ( x + 8 ) ( x - 5 ) = 0

Il suffit que l'un des membres du produit soit nul.

x + 8 = 0

⇔ x = -8

x - 5 = 0

⇔ x = 5

S = { -8, 5 }

b/   5x( 4 - x ) = 0

5x = 0

⇔ x = 0

4 - x = 0

⇔ x = 4

S = { 0 , 4 }

c/     ( x + 3 )² = 0

x + 3 = 0

⇔ x = -3

S = { -3 }

57/a       ( 2x + 7 ) (3 x - 12 ) = 0

2x + 7 = 0

⇔ 2x = -7

⇔ x = -7/2

3x -12 = 0

⇔ 3x = 12

⇔ x = 4

S =  { -7/2 , 4 }

b/ (5y - 2 ) ( 6y + 9 ) = 0

5y -2 = 0

⇔ 5y = 2

⇔ y = 2/5

6y + 9 = 0

⇔ 6y = -9

⇔ y = -9/6 = -3/2

S =  { -3/2 , 2/5 }

58/      2x (4x - 5 ) = 0

2x = 0

⇔ x = 0

4x - 5 = 0

⇔ 4x = 5

⇔ x =5/4

S = { 0, 5/4 }

b/  ( 3 - 2n ) ( n + 4 ) = 0

⇔ 3 - 2n = 0

⇔ - 2n = -3

⇔ 2n = 3

⇔ n = 3/2

n + 4 = 0

⇔ n = -4

S = { -4, 3/2 }

59/a       ( 2x + 1 ) ( 3x - 5 ) = 0

    2x +1 = 0

⇔ 2x = -1

⇔ x = -1/2

    3x - 5 = 0

⇔ 3x = 5

⇔ x = 5/3

S =  { -1/2 , 5/3 }

Ce sont des nombres rationnels, quotient de deux entiers relatifs.

2 ( 4y - 3 ) ( 6y + 1 ) = 0

   4y - 3 = 0

⇔ 4y = 3

⇔ y = 3/4

    6y + 1 = 0

⇔ 6y = -1

⇔ y = -1/6

S = {-1/6 , 3/4 }

Ce sont des nombres rationnels, quotient de deux entiers relatifs.

60/   x² - 5x = 0

  ⇔ x ( x -5 ) = 0

S =   {0 , 5}

6x² - 18x = 0

⇔ 6x ( x -3 ) = 0

S =   { 0, 3}

61/     x² - 4 = 0

(x - 2 ) ( x + 2 ) = 0

S = {  -2, 2  }

x² - 6x + 9 = 0

⇔ x² - 3x - 3x + 9 = 0

⇔ x ( x -3 ) - 3 ( x - 3 ) = 0

⇔ (x - 3 ) (x - 3) = 0

S = { 3}