# Solution May 30, 2007

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### Problem

Let a,b,c,d be positive reals such that *a* + *b* + *c* + *d* = 1.

Prove that: .

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### Solution

Let ,
and . By the power mean inequality (*http://planetmath.org/encyclopedia/GeneralMeansInequality.html*), we have

- .

This implies

Using , this is equivalent to

q.e.d.