bonjour
A = ( 3 x - 2 )² - 16
a) A = 9 x² - 12 x + 4 - 16 = 9 x² - 12 x - 12
b ) A = ( 3 x - 2 - 4 ) ( 3 x - 2 + 4 ) = ( 3 x - 6 ) ( 3 x + 2 ) = 3 ( x - 2 ) ( 3 x + 2 )
c ) 9 x² - 12 x - 12
α = 12/18 = 2 /3
β = 9 *(2/3)² - 12*2/3 - 12 = 9*4/9 - 24/3 - 12 = 36/9 - 8 - 12 = 4 - 8 - 12 = - 16
A = 9 ( x - 2/3 )² - 16
f (x)= ( 3 x - 2 )² - 15
EDef = R
f ( 0 ) = ( - 2 )² - 15 = 4 - 15 = - 11
f ( - 1 ) = ( - 3 - 2 )² - 15 = ( - 5 )² - 15 = 25 - 15 = 10
f ( 2/3 ) = ( 6/3 - 6/3 ) ² - 15 = - 15
f ( √2) = ( 3 √2 - 2 )² - 16 = 18 - 12√2 + 4 - 16 = - 12 √2 + 6
antécédents de 0
( 3 x - 2 - 4 ) ( 3 x - 2 + 4 ) = 0
( 3 x - 6 ) ( 3 x + 2 ) = 0
x = 2 ou - 2 /3
( 3 x - 2 )² - 16 = - 16
( 3 x- 2 )² = 0
x = 2/3
( 3 x - 2)² - 16 = - 25
( 3 x - 2 )² = - 25 + 16
( 3 x - 2 )² = - 9
pas d antécédent
d) ( 3 x - 6 ) ( 3 x + 2 ) = 0
s'annule en 2 et - 2 /3
x - ∞ - 2/3 2 + ∞
3 x - 6 - - 0 +
3 x + 2 - 0 + +
produit + 0 - 0 +
] - ∞ ; - 2/3 [ ∪ ] 2 ; + ∞ [
bonne journée
