MathDB

1

Part of VMEO I 2004

Problems(1)

sum \sqrt{x+ (y-z)^2 /12 } <= \sqrt3 if x, y, z>=0, x + y + z = 1,

Source: 2004 VMEO I p1 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2461015_vmeo__vietnam_mathematical

9/26/2021
Let x,y,zx, y, z be non-negative numbers, so that x+y+z=1x + y + z = 1. Prove that x+(y−z)212+y+(x−z)212+z+(x−y)212≤3\sqrt{x+\frac{(y-z)^2}{12}}+\sqrt{y+\frac{(x-z)^2}{12}}+\sqrt{z+\frac{(x-y)^2}{12}}\le \sqrt{3}
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