Let \(p,q,r,s\) be real numbers such that \(p +q + r + s = 8\) and \(pq + pr + ps + qr + qs + rs = 12.\) Find the largest possible value of \(s.\)
Again Lagrange multipliers make short work of this. This problem requires the use of 2 of them.
\(s = 2+3\sqrt{2} \text{ is the largest value of }s \text{ satisfying the constraints}\)
