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