Bonjour vous pouvez m’aider pour le 73,74,75 j’ai essayé mais j’arrive pas vous pouvez m’aider svp

Réponse :

a^2 - b^2 = (a - b)(a + b)

a^2 - 2ab + b^2 = (a - b)^2

a^2 + 2ab + b^2 = (a + b)^2

Un produit de facteur est nul si et seulement si au moins un de ses facteurs est nul

Explications étape par étape

Bonjour

Résoudre en ramenant à une équation produit nul :

Exercice 73 :

x^2 - 36 = 0

x^2 - 6^2 = 0

(x - 6)(x + 6) = 0

x - 6 = 0 ou x + 6 = 0

x = 6 ou x = -6

4x^2 - 1 = 0

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

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

2x - 1 = 0 ou 2x + 1 = 0

2x = 1 ou 2x = -1

x = 1/2 ou x = -1/2

25x^2 - 100 = 0

(5x)^2 - 10^2 = 0

(5x - 10)(5x + 10) = 0

5(x - 2) * 5(x + 2) = 0

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

x - 2 = 0 ou x + 2 = 0

x = 2 ou x = -2

5x^2 - 3x = 0

5x * x - 3 * x = 0

x(5x - 3) = 0

x = 0 ou 5x - 3 = 0

x = 0 ou 5x = 3

x = 0 ou x = 3/5

Exercice 74 :

(2x + 3)(x - 2) + 2(x - 2) = 0

(x - 2)(2x + 3 + 2) = 0

(x - 2)(2x + 5) = 0

x - 2 = 0 ou 2x + 5 = 0

x = 2 ou 2x = -5

x = 2 ou x = -5/2

25x^2 - 30x + 9 = 0

(5x)^2 - 2 * 5x * 3 + 3^2 = 0

(5x - 3)^2 = 0

5x - 3 = 0

5x = 3

x = 3/5

(3x + 1)(5x - 1) - 4(5x - 1) = 0

(5x - 1)(3x + 1 - 4) = 0

(5x - 1)(3x - 3) = 0

(5x - 1) * 3(x - 1) = 0

3(5x - 1)(x - 1) = 0

5x - 1 = 0 ou x - 1 = 0

5x = 1 ou x = 1

x = 1/5 ou x = 1

(3x + 1)^2 - 49 = 0

(3x + 1)^2 - 7^2 = 0

(3x + 1 - 7)(3x + 1 + 7) = 0

(3x - 6)(3x + 8) = 0

3(x - 2)(3x + 8) = 0

x - 2 = 0 ou 3x + 8 = 0

x = 2 ou 3x = -8

x = 2 ou x = -8/3

Exercice 75

x(2x - 5) = 2(2x - 5)

x(2x - 5) - 2(2x - 5) = 0

(2x - 5)(x - 2) = 0

2x - 5 = 0 ou x - 2 = 0

2x = 5 ou x = 2

x = 5/2 ou x = 2

(5x + 2)(2x - 3) = 4x^2 - 12x + 9

(5x + 2)(2x - 3) = (2x)^2 - 2 * 2x * 3 + 3^2

(5x + 2)(2x - 3) = (2x - 3)^2

(5x + 2)(2x - 3) - (2x - 3)^2 = 0

(2x - 3)(5x + 2 - 2x + 3) = 0

(2x - 3)(3x + 5) = 0

2x - 3 = 0 ou 3x + 5 = 0

2x = 3 ou 3x = -5

x = 3/2 ou x = -5/3

5x^2 = 8x(x + 1)

8x^2 + 8x - 5x^2 = 0

3x^2 + 8x = 0

x * 3x + x * 8 = 0

x(3x + 8) = 0

x = 0 ou 3x + 8 = 0

x = 0 ou 3x = -8

x = 0 ou x = -8/3

(2x + 1)^2 = 9

(2x + 1)^2 - 3^2 = 0

(2x + 1 - 3)(2x + 1 + 3) = 0

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

2(x - 1) * 2(x + 2) = 0

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

x - 1 = 0 ou x + 2 = 0

x = 1 ou x = -2

(4x + 7)^2 = (x - 2)^2

(4x + 7)^2 - (x - 2)^2 = 0

(4x + 7 - x + 2)(4x + 7 + x - 2) = 0

(3x + 9)(5x + 5) = 0

3(x + 3) * 5(x + 1) = 0

15(x + 3)(x + 1) = 0

x + 3 = 0 ou x + 1 = 0

x = -3 ou x = -1

(7x - 2)^2 - 1 = 80

(7x - 2)^2 - 1 - 80 = 0

(7x - 2)^2 - 81 = 0

(7x - 2)^2 - 9^2 = 0

(7x - 2 - 9)(7x - 2 + 9) = 0

(7x - 11)(7x + 7) = 0

(7x - 11) * 7(x + 1) = 0

7(7x - 11)(x + 1) = 0

7x - 11 = 0 ou x + 1 = 0

7x = 11 ou x = -1

x = 11/7 ou x = -1