MathDB
square root begs for a well known inequality

Source: Romanian IMO Team Selection Test TST 1996, problem 13

September 27, 2005
inequalitiesinequalities proposed

Problem Statement

Let x1,x2,…,xn x_1,x_2,\ldots,x_n be positive real numbers and xn+1=x1+x2+⋯+xn x_{n+1} = x_1 + x_2 + \cdots + x_n . Prove that ∑k=1nxk(xn+1−xk)≤∑k=1nxn+1(xn+1−xk). \sum_{k=1}^n \sqrt { x_k (x_{n+1} - x_k)} \leq \sqrt { \sum_{k=1}^n x_{n+1}(x_{n+1}-x_k)}. Mircea Becheanu
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