USAMO 1977 Problem 5 Day 2 The positive reals v,w,x,y,z\mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{y}, \mathrm{z}v,w,x,y,z satisfy 0<h≤v,w,x,y,z≤k0<\mathrm{h} \leq \mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{y}, \mathrm{z} \leq \mathrm{k}0<h≤v,w,x,y,z≤k. Show that (v+w+x+y+z)(1/v+1/w+1/x(\mathrm{v}+\mathrm{w}+\mathrm{x}+\mathrm{y}+\mathrm{z})(1 / \mathrm{v}+1 / \mathrm{w}+1 / \mathrm{x}(v+w+x+y+z)(1/v+1/w+1/x +1/y+1/z)≤25+6((h/k)−(k/h))2+1 / \mathrm{y}+1 / \mathrm{z}) \leq 25+6(\sqrt{ }(\mathrm{h} / \mathrm{k})-\sqrt{ }(\mathrm{k} / \mathrm{h}))^{2}+1/y+1/z)≤25+6((h/k)−(k/h))2. When do we have equality? 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 PreviousProblem 4 Locator usamo/1977/p5 · Tag 7F6TYW1BA3 · Edit this page on GitHub · Keys: j next, k previous