Réponse :
Explications étape par étape :
bonjour
f (x)= ( - 1 + 3 x )² - ( - x + 2 )²
1. f (x) = ( 1 - 6 x + 9 x² ) - ( x² - 4 x + 4 )
f (x) = 9 x² - 6 x + 1 - x² + 4 x - 4
f (x) = 8 x² - 2 x - 3
2. f (x) = ( - 1 + 3 x - x + 2 ) ( - 1 + 3 x + x - 2 )
f (x) = ( 2 x + 1 ) ( 4 x - 3 )
3. f (x) = 8 ( x - 1/8)² - 25 /8
f (x) = 8 ( x² - 2 x /8 + 1 /64 ) - 25/8
f (x) = 8 x² - 16 x /8 + 8/64 - 25/8
f (x) = 8 x² - 2 x + 8/64 - 200/64
f (x) = 8 x² - 2 x - 3
f (x) = 0
( 2 x + 1 ) ( 4 x- 3 ) = 0
x = - 1/2 ou 3 /4
f (x) = - 25/8
8 ( x - 1/8)² - 25 /8 = - 25/8
8 ( x - 1/ 8)² = 0
x = 1/8
f x( ) = ( 2 x + 1 )
( 2 x + 1 ) ( 4 x - 3 ) = 2 x + 1
(2 x + 1 ) ( 4 x- 3) - ( 2 x + 1 ) = 0
( 2 x + 1 ) ( 4 x - 3 - 1 ) = 0
( 2 x + 1 ) ( 4 x - 4 ) = 0
x = - 1/2 ou 1
