MathDB

2

Part of 2001 China Second Round Olympiad

Problems(1)

Find extremes of \sum x_i

Source: Chinese National Competition 2001

1/28/2005
If nonnegative reals x1,x2,…,xnx_1, x_2, \ldots, x_n satisfy ∑i=1nxi2+2∑1≤k<j≤nkjxkxj=1 \sum_{i=1}^n x_i^2 + 2\sum_{1 \leq k < j \leq n} \sqrt{\frac{k}{j}}x_kx_j = 1 what are the minimum and maximum values of ∑i=1nxi\sum_{i=1}^n x_i?
inequalitiesinequalities proposed