Problem

Source: Iranian National Olympiad (3rd Round) 2007

Tags: inequalities, inequalities proposed



Find the largest real $ T$ such that for each non-negative real numbers $ a,b,c,d,e$ such that $ a+b=c+d+e$: \[ \sqrt{a^{2}+b^{2}+c^{2}+d^{2}+e^{2}}\geq T(\sqrt a+\sqrt b+\sqrt c+\sqrt d+\sqrt e)^{2}\]