bonjour
f (x ) = - x² + 10 x - 21
f (x) = 4 - ( x - 5 )²
= 4 - ( x² - 10 x + 25 )
= 4 - x² + 10 x - 25
= - x² + 10 x - 21
4 - ( x - 5 )² = ( 2 + x - 5 ) ( 2 - x + 5 ) = ( x - 3 ) ( - x + 3 )
S = ( x - 3 )² = x² - 6 x + 9
S ' = ( x - 3 ) ( x - 5 ) = x² - 5 x - 3 x + 15 = x² - 8 x + 15
x² - 6 x + 9 - 2 ( x² - 8 x + 15 )
= x² - 6 x + 9 - 2 x² + 16 x - 30
= - x² + 10 x - 21
( x - 3 ) ( - x + 3 ) = 0
x = 3