on a : lxl ≤ 1/2 et lYl ≤ 1
Démontrez que : l4x²Y-Y-xl ≤ 17/16




Sagot :

on a : lxl ≤ 1/2 et lYl ≤ 1
-1/2
≤ x ≤ 1/2 et -1 ≤ y ≤ 1
0
≤ x² ≤ 1/4
0
≤ 4x² ≤ 1
-1
≤ 4x²y ≤ 1
 
-3/2
≤ x+y ≤ 3/2
-3/2
≤ -x-y ≤ 3/2
-5/2
≤ 4x²y-x-y ≤ 5/2
 l4x²Y-Y-xl ≤ 5/2
 l4x²Y-Y-xl ≤ 17/16