Home Competitions AUSTRIAN-POLISH 1984 Problem 3
AUSTRIAN-POLISH 1984 Problem 3
Show that for n > 1 n>1 n > 1 k , x 1 , x 2 , . . . , x n k,x_{1},x_{2},...,x_{n} k , x 1 , x 2 , ... , x n f ( x 1 − x 2 ) x 1 + x 2 + f ( x 2 − x 3 ) x 2 + x 3 + . . . + f ( x n − x 1 ) x n + x 1 ≥ n 2 2 ( x 1 + x 2 + . . . + x n ) \frac{f(x_{1}-x_{2})}{x_{1}+x_{2}}+\frac{f(x_{2}-x_{3})}{x_{2}+x_{3}}+...+\frac{f(x_{n}-x_{1})}{x_{n}+x_{1}}\geq \frac{n^2}{2(x_{1}+x_{2}+...+x_{n})} x 1 + x 2 f ( x 1 − x 2 ) + x 2 + x 3 f ( x 2 − x 3 ) + ... + x n + x 1 f ( x n − x 1 ) ≥ 2 ( x 1 + x 2 + ... + x n ) n 2 f ( x ) = k x f(x)=k^x f ( x ) = k x
Dataset text AI-MO AoPS . Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.
Add a solution
Similar problems
These problems have the most words in common with this statement.
Locator austrian-polish/1984/p3 · Tag RX52JH6MBT · Edit this page on GitHub · Keys: j next, k previous