equation avec factorisation bonsoir comment resoudre les equation suivante en detaillant toute les etapes : A = 25x²-81-(x+1)(5x+9) B= 25x²+30x+9=(5x-1)(5x+3) C

Bonsoir,

Factoriser et résoudre :

A = 25x²-81-(x+1)(5x+9)

A = (5x)² - 9² - (x + 1)(5x + 9)

A = (5x - 9)(5x + 9) - (x + 1)(5x + 9)

A = (5x + 9)(5x - 9 - x - 1)

A = (5x + 9)(4x - 10)

A = 2(5x + 9)(2x - 5) = 0

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

5x + 9 = 0 ou 2x - 5 = 0

5x = -9 ou 2x = 5

x = -9/5 ou x = 5/2

B= 25x²+30x+9=(5x-1)(5x+3)

B = (5x)² + 2 * 5x * 3 + 3² = (5x - 1)(5x + 3)

(5x + 3)² = (5x - 1)(5x + 3)

(5x + 3)² - (5x - 1)(5x + 3) = 0

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

(5x + 3)(4) = 0

4(5x + 3) = 0

5x + 3 = 0

5x = -3

x = -3/5

C= (7x+3)(4x-1)=-49x²+42x-9

(7x + 3)(4x - 1) = (-7x - 3)²

(7x + 3)(4x - 1) + (7x + 3)² = 0

(7x + 3)(4x - 1 + 7x + 3) = 0

(7x + 3)(11x + 2) = 0

7x + 3 = 0 ou 11x + 2 = 0

7x = -3 ou 11x = -2

x = -3/7 ou x = -2/11