MathDB
Inequality

Source: 1998 National High School Mathematics League, Exam Two, Problem 2

March 9, 2020
inequalities

Problem Statement

Let a1,a2,⋯ ,an,b1,b2,⋯ ,bna_1,a_2,\cdots,a_n,b_1,b_2,\cdots,b_n are real numbers in [1,2][1,2]. If ∑i=1nai2=∑i=1nbi2\sum_{i=1}^{n}a_i^2=\sum_{i=1}^{n}b_i^2, prove that ∑i=1nai3bi≤1710∑i=1nai2.\sum_{i=1}^{n}\frac{a_i^3}{b_i}\leq\frac{17}{10}\sum_{i=1}^{n}a_i^2. Find when the equality holds.
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