Explications étape par étape :
a) 9x² = 64.
⇔ 9x² - 64 = 0 identité remarquable a² - b² = ( a - b ) ( a + b )
⇔ ( 3x - 8 ) ( 3x + 8 ) = 0 Equation produit
3x - 8 = 0 ou 3x + 8 = 0
⇔ 3x = 8 ⇔ 3x = -8
⇔ x = 8/3 ⇔ x = -8/3
S = { -8/3 , 8/3 }
b) 100x² = 81
⇔ 100 x² - 81 = 0 identité remarquable a² - b² = ( a - b ) ( a + b )
⇔ ( 10x - 9 ) ( 10x + 9 ) = 0
10x - 9 = 0 ou 10x + 9 = 0
⇔ 10x = 9 ⇔ 10x = -9
⇔ x = 9/10 ⇔ x = -9/10
S = { -9/10 ; 9/10 }
c) 4x ² - 36 = 0 identité remarquable a² - b² = ( a-b) ( a + b )
⇔ ( 2x - 6 ) ( 2x + 6 ) = 0
2x - 6 = 0 ou 2x + 6 = 0
⇔ 2x = 6 ⇔ 2x = -6
⇔ x = 3 ⇔ x = -3
S = { -3 ; 3 }
d) 25x ² - 16 = 0 identité remarquable a² - b² = ( a - b) ( a + b )
⇔ ( 5x - 4 ) ( 5x + 4 ) = 0
5x - 4 = 0 ou 5x + 4 = 0
⇔ 5x = 4 ⇔ 5x = -4
⇔ x = 4/5 ⇔ x = -4/5
S = { -4/5 ; 4/5 }
