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China Northern Mathematical Olympiad 2014 , Problem 6

Source: China Sijiazhuang , Aug 2014

August 12, 2014
inequalitiesinequalities proposed

Problem Statement

Let x,y,z,wx,y,z,w be real numbers such that x+2y+3z+4w=1x+2y+3z+4w=1. Find the minimum of x2+y2+z2+w2+(x+y+z+w)2x^2+y^2+z^2+w^2+(x+y+z+w)^2.
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