bonjour
f (x) = ( x - 3 )² - 16
f (x) = x² - 6 x + 9 - 16 = x² - 6 x - 7
f (x) = ( x - 3 - 4 ) ( x - 3 + 4) = ( x - 7 ) ( x + 1 )
f (3) = ( 3 - 7 ) ( 3 + 1 ) = - 4 x 4 = - 16
f ( - 3 ) = ( - 3 - 7 ) ( - 3 + 1 ) = - 10 x - 2 = 20
f ( 3 + √2) = ( 3 + √2 - 7 ) ( 3 + √2 + 1 )
= 9 + 3 √2 + 3 + 3 √2 + √4 + √2 - 21 - 7 √2 - 7
= 12 + 6 √2 + 2 + √2 - 28 - 7 √2
= - 14
f (x) = - 16
( x - 3 )² - 16 = - 16
( x - 3 )² = 16 - 16 = 0
( x - 3 )² = 0
donc x = 3
