a and b are real numbers such that a2+b2=1, and always satisfy
1+a21+1+b21+1+ab1≥1+z(a+b)2x.
Find ⌊zx⌋ when the value of the LHS of the above inequality is the least.
Details and Assumptions:
- x and z are positive integers.
- ⌊⋅⌋ denotes the greatest integer function.