Réponse :
bonjour
f (x) = ( 2 x - 3 )² - 49
1. f (x) = 4 x² - 12 x + 9 - 49 = 4 x² - 12 x - 40
2. f (x) = ( 2 x - 3 - 7 ) ( 2 x - 3 + 7 ) = ( 2 x - 10 ) ( 2 x + 4 )
3. f ( - 1 ) = 4 ( - 1 )² - 12 ( - 1 ) - 40 = 4 + 12 - 40 = - 24
f ( √2) = 4 ( √2)² - 12 √2 - 40 = 8 - 12 √2 - 40 = - 32 - 12√2
f (x) = 0
( 2 x - 10 ) ( 2 x + 4 ) = 0
x = 10/2 = 5 ou - 4/2 = - 2
f (x) = - 40
4 x² - 12 x - 40
4 x² - 12 x - 40 = - 40
4 x² - 12 x = 0
4 x ( x - 3 ) = 0
x = 0 ou 3
Explications étape par étape :