bonjour
h (x) = ( 2 x + 1 )² - ( x - 2 )²
a) h (x) = 4 x² + 4 x + 1 - ( x² - 4 x + 4 ) = 4 x² + 4 x + 1 - x² + 4 x - 4
= 3 x² + 8 x - 3
b ) h (x) = ( 2 x + 1 + x - 2 ) ( 2 x + 1 - x + 2 ) = ( 3 x - 1 ) ( x + 3 )
h ( 0 ) = ( - 1 ) ( 3 ) = - 3
h ( √2) = ( 3 √2 - 1 ) ( √2 + 3 ) = 3 √4 + 9 √2 - √2 - 3 = 6 + 9 √2 - 3
= 3 + 9 √ 2
h ( x) = - 3
3 x² + 8 x - 3 = - 3
3 x² + 8 x = 0
x ( 3 x + 8 ) = 0
x = 0 ou - 8/3
h (x) = 0
( 3 x - 1 ) ( x + 3 ) = 0
x = 1/3 ou - 3
h (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
