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# help

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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

#1
+6046
+1

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
+6046
+1
$$s = 2+3\sqrt{2} \text{ is the largest value of }s \text{ satisfying the constraints}$$