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Pairwise Products
Problem
For any set of real numbers, R = {x, y, z}, let sum of pairwise products,
S = xy + xz + yz.
Given that x + y + z = 1, prove that S 
1/3.
Problem ID: 224 (24 May 2005) Difficulty: 4 Star
For any set of real numbers, R = {x, y, z}, let sum of pairwise products,
S = xy + xz + yz.
Given that x + y + z = 1, prove that S 1/3.
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