olymmath

USAMO 1980 Problem 5

  • Day 2

If x,y,zx, y, z are reals such that 0≤x,y,z≤10 \leq x, y, z \leq 1, show that x/(y+z+1)+y/(z+x+1)+z/(x+y+1)≤1−(1−x /(y+z+1)+y /(z+x+1)+z /(x+y+1) \leq 1-(1- x)(1−y)(1−z)\mathrm{x})(1-\mathrm{y})(1-\mathrm{z}).

Dataset text NuminaMath olympiads. 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

Locator usamo/1980/p5 · Tag 4D04DFGSVD · Edit this page on GitHub · Keys: j next, k previous