bonsoir
f (x) = ( 2 x + 1 )² - ( x - 2 )²
f (x ) = 4 x² + 4 x + 1 - ( x² - 4 x + 4 )
f (x) = 4 x² + 4 x + 1 - x² + 4 x - 4
f (x) = 3 x² + 8 x - 3
f (0) = - 3
f ( √2) = 3 ( √2)² + 8 √2 - 3 = 18 + 8 √2 - 3 = 15 + 8 √ 2
f (x) = - 3
3 x² + 8 x - 3 = - 3
3 x² + 8 x = 0
x ( 3 x + 8 ) = 0
x = 0 ou - 8/3
f (x) = x + 3
3 x² + 8 x - 3 = x + 3
3 x² + 8 x - x = 3 + 3
3 x² + 7 x = 6
3 x² + 7 x - 6 = 0
Δ = 49 - 4 ( 3 * - 6 ) = 49 + 72 = 121
x 1 = ( - 7 - 11 ) / 6 = - 18/6 = - 3
x 2 = ( - 7 + 11 ) /6 = 4 /6 = 2/3
S { - 3 ; 2/3 }
