We are given 4 lines with equations:
- y=(a+b(1+a2)2+3a2+3b2(1+a2)2+b(6a+6a3))min2
- y=(c2d+cc2d2−2c2d+2c2+2cd−2c+1)min+3−8
- y=[e]x2
- y=21[e]x2
With a,b,c,d>0,e≥1 .
The area bounded by the given lines and the curves when obtain a maximum value of M, with M=a2a1(a3−1)(a4a5−1).
Find a1+a2+a3+a4+a5.
Details and Assumptions:
- [.] denote the greatest integer function.
- (f(x))min denote the minimum value of f(x).