If m and M are the minimum and the maximum values of 4+12sin²2x - cos4x, x∈R, then M-m is equal to:

4+12sin²2x - cos4x
4+2(1-cos2x)cos2x - cos4x - cos2x² + 1
16 - (cos2x - 4)² + 1
16 - (cos2x - 4)² + 1
Since -1 ≤ cos2x ≤ 1
-4 ≤ cos2x -4 ≤ -3
0 ≤ (cos2x - 4)² ≤ 16
-16 ≤ -(cos2x - 4)² ≤ 0
17 - 16 ≤ 16 -(cos2x - 4)² ≤ 17
1 ≤ 16 - (cos2x - 4)² ≤ 17
Let y = 16-(cos2x-4)²
When (cos2x - 4)² = 0, y = 17
When (cos2x - 4)² = 16, y = 1
M = 17
m = 1
M - m = 17 - 1 = 16