bonjour
A(x) = ( 4 x + 1 )² - ( 6 x - 11 )²
1. 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
2. A (x) = ( 4 x + 1 + 6 x - 11 ) ( 4 x + 1 - 6 x + 11 )
A (x) = ( 10 x - 10 ) ( - 2 x + 12 )
3. A ( x) = - 20 ( x - 7/2)² + 125
A (x) = - 20 ( x² - 14 x /2 + 49/4 ) + 125
A (x) = - 20 x² + 140 x - 245 + 125
A (x) = - 20 x² + 140 x - 120
4 . A (x) = 0
( 10 x - 10 ) ( - 2 x + 12 ) = 0
soit 10 x - 10 = 0 et x = 1
soit - 2 x + 12 = 0 et x = 6
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) = 45
- 20 x² + 140 x - 120 = 45
- 20 x² + 140 x = 45 + 120
- 20 x² + 140 x = 165
- 20 x² + 140 x - 165 = 0
Δ = 19 600 - 4 ( - 20 * - 165) = 6 400
x ₁ = ( - 140 - 80 ) / - 40 = 5 .5
x ₂ = ( - 140 + 80 ) / - 40 = 1.5
S ( 1.5 ; 5.5 )
A (x) = - 20 x²
- 20 x² + 140 x - 120 = - 20 x²
- 20 x² + 20 x² + 140 x - 120 = 0
140 x = 120
x = 120/140 = 6/7
