MathDB

1.1

Part of 2014 Saudi Arabia Pre-TST

Problems(1)

\sqrt{a^2_j-a^2_k < \frac{1}{\sqrt{n} +\sqrt{n - 1}}

Source: 2014 Saudi Arabia Pre-TST 1.1

9/13/2020
Let a1,a2,...,a2na_1, a_2,...,a_{2n} be positive real numbers such that ai+an+i=1a_i + a_{n+i} = 1, for all i=1,...,ni = 1,...,n. Prove that there exist two different integers 1≤j,k≤2n1 \le j, k \le 2n for which aj2−ak2<1n+n−1\sqrt{a^2_j-a^2_k} < \frac{1}{\sqrt{n} +\sqrt{n - 1}}
algebrainequalities