Réponse :
bonjour
A (x) = ( 4 x + 1 )² - ( 6 x - 11 )²
A (x) = 16 x² + 8 x + 1 - ( 36 x² - 132 x + 121 )
A (x) = 16 x² + 8 x + 1 - 36 x² + 132 x - 121
A (x) = - 20 x² + 140 x - 120
A (x) = ( 4 x + 1 + 6 x - 11 ) ( 4 x + 1 - 6 x + 11 )
A (x) = ( 10 x - 10 ) ( - 2 x + 15 )
a (x) = 10 ( x - 1 ) ( - 2 x + 15 )
A (x) = - 20 ( x - 7/2 )² + 125
A (x) = - 20 ( x² - 14 x /2 + 49/4 ) + 125
a (x) = - 20 x² + 140 x - 980/4 + 125
A (x) = - 20 x² + 140 x - 245 + 125
A (x) = - 20 x² + 140 x - 120
A (x) = 0
10 ( x - 1 ) ( - 2 x + 15 ) = 0
x = 1 ou 15/2 = 7.5
A (x) = 45
- 20 x² + 140 x - 120 = 45
- 20 x² + 140 x - 120 - 45 = 0
- 20 x² + 140 x - 165 = 0
Δ = 140² - 4 ( - 20 * - 165 ) = 19 600 - 13 20 = 6 400 = 80 ²
x 1 = ( - 140 - 80 ) / - 40 = - 220/ - 40 = 5.5
x2 = ( - 140 + 80 ) / - 40 = - 60/ - 40 = 3 /2
A (x) = - 120
- 20 x² + 140 x - 120 = - 120
- 20 x² + 140 x - 120 + 120 = 0
- 20 x ( x - 7 ) = 0
x = 0 ou 7
A (x) = - 20 x²
- 20 x² + 140 x - 120 = - 20 x²
- 20 x² + 20 x² + 140 x - 120 = 0
140 x = 120
x = 6/7
Explications étape par étape
