MathDB
yet another classical inequality

Source: Romanian Nationals RMO 2005 - grade 8, problem 4

March 31, 2005
inequalitiesalgebra

Problem Statement

a) Prove that for all positive reals u,v,x,yu,v,x,y the following inequality takes place: ux+vy≥4(uy+vx)(x+y)2. \frac ux + \frac vy \geq \frac {4(uy+vx)}{(x+y)^2} . b) Let a,b,c,d>0a,b,c,d>0. Prove that ab+2c+d+bc+2d+a+cd+2a+b+da+2b+c≥1. \frac a{b+2c+d} + \frac b{c+2d+a} + \frac c{d+2a+b} + \frac d{a+2b+c} \geq 1. Traian Tămâian
Back to ProblemsView on AoPS