Réponse :
Explications étape par étape
1/ f(x) = ( x - 5 )² - 36
1a/ f(x) = x² - 10x + 25 - 36 ( x - 5 )² identité remarquable
⇔ f(x) = x² - 10x - 11
b/ f(x) = ( x - 5 )² - 36 forme a² - b² = ( a + b ) ( a - b )
⇔ f(x) = ( x - 5 - 6 ) ( x - 5 + 6 )
⇔ f(x) = ( x - 11 ) ( x + 1 )
2/a/ f(x ) = 0
f(x) = ( x - 11 ) ( x + 1 ) = 0
x - 11 = 0 ou x + 1 = 0
x = 11 x = -1
S = { -1 ; 11 }
b/ f(x) = - 36
f(x) = ( x - 5 )² - 36 = -36
⇔ f(x) = ( x - 5 )² = 0
⇔ f(x) = x² - 10x + 25 = 0
⇔ f(x) = x² - 5x - 5x + 25 = 0
⇔ f(x) = x ( x - 5 ) - 5 ( x - 5 ) = 0
⇔ f(x) = ( x -5 ) ( x - 5 )
x - 5 = 0
⇔ x = 5
S = { 5 }
c/ f(x) = -11
f(x) = x² - 10x - 11 = -11
⇔ f(x) = x² - 10x = 0
⇔ f(x) = x ( x - 10 )
x = 0 ou x = 10
S = { 0 ; 10 }
d/ f(x) = - 10x
⇔ f(x) = x² - 10x - 11 = -10x
⇔ f(x) = x² - 11 = 0
⇔ f(x) = ( x - √11 ) ( x + √11 ) = 0
x - √11 = 0 ou x + √11 = 0
⇔ x = √11 ⇔ x = -√11
S = { -√11, √11 }
