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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 \(s.\)

 Apr 9, 2019

Best Answer 

 #1
avatar+6046 
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Again Lagrange multipliers make short work of this.  This problem requires the use of 2 of them.

 

 

\(s = 2+3\sqrt{2} \text{ is the largest value of }s \text{ satisfying the constraints}\)

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 Apr 9, 2019
 #1
avatar+6046 
+1
Best Answer

Again Lagrange multipliers make short work of this.  This problem requires the use of 2 of them.

 

 

\(s = 2+3\sqrt{2} \text{ is the largest value of }s \text{ satisfying the constraints}\)

Rom Apr 9, 2019

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