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

2015 JBMO Shortlist, A3
If $a,b,c$ are positive real numbers prove that: $\frac{a}{b}+\sqrt{\frac{b}{c}}+\sqrt[3]{\frac{c}{a}}>2.$
qjyt sbyt AM-GM inequality algebra inequalities

1979 IMO Longlists, 40
A polynomial $P(x)$ has degree at most $2k$, where $k = 0, 1,2,\cdots$. Given that for an integer $i$, the inequality $-k \le i \le k$ implies $|P(i)| \le 1$, prove that for all real numbers $x$, with $-k \le x \le k$, the following inequality holds: \[|P(x)| < (2k + 1)\dbinom{2k}{k}\]
qjyt sbyt algebra inequalities polynomials