Réponse :
Explications étape par étape :
f(x) = (x – 5)² – 36
1) a) f(x) = (x – 5)² – 36
f(x) = x² – 10x + 25 – 36 = x² – 10x – 11
b) f(x) = (x – 5)² – 36
f(x) = (x – 5 – 6)(x – 5 + 6) = (x – 11)(x + 1)
2) a) f(x) = (x – 11)(x + 1)
f(5) = (5 - 11)(5 + 1) = (-6)*(6) = - 36
b) (x – 11)(x + 1) = 0
soit x – 11 = 0 donc x = 11 soit x + 1 = 0 donc x = - 1
c) x² – 10x – 11 = - 11 x² – 10x = - 11 + 11 x² – 10x = 0
x(x - 10) = 0 soit x = 0 soit x - 10 = 0 donc x = 10
d) (x – 5)² – 36 = - 40 (x – 5)² = 36 - 40 (x – 5)² = - 4 impossible un carré est toujours positif
e) x² – 10x – 11 = - 10x x² – 11 = - 10x + 10x x² – 11 = 0
x² = 11 x = 3,3