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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