Réponse:
en déduire les valeurs de n tel que n^3–n divise n+2 €N.
division euclidienne :
n+2
n³ – n |_____________________
-n³ – 2n² n² – 2n – 4 + 4 – 5
_______
–2n² –n
+2n² – 4n
________
–4n –n
+ 4n + 8
___________
8 – n
–8 – 4n
_________
–5n
+ 5n + 10
________
10
donc n³ - n = n² – 2n – 5 + (10/n+2)
n² – 2n – 5 = 0
delta= (-2)² – 4(1)(–5)
= 20 + 4 = 24
√ delta = 2√6
N1 = (2– 2√6)/2
= 1–√6
