This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2017 China National Olympiad, 6
Tags: BPSQ , China , PRC , inequalities , Inequality proposed , convex-concave inequalities , sqing orz
Given an integer $n \geq2$ and real numbers $a,b$ such that $0<a<b$. Let $x_1,x_2,\ldots, x_n\in [a,b]$ be real numbers. Find the maximum value of $$\frac{\frac{x^2_1}{x_2}+\frac{x^2_2}{x_3}+\cdots+\frac{x^2_{n-1}}{x_n}+\frac{x^2_n}{x_1}}{x_1+x_2+\cdots +x_{n-1}+x_n}.$$

2016 Bulgaria JBMO TST, 2
Tags: Inequality proposed , inequalities
a, b, c are positive real numbers and a+b+c=k. Find the minimum value of $ b^2/(ka+bc)^1/2+c^2/(kb+ac)^1/2+a^2/(kc+ab)^1/2 $