Advance Happy New Year 2015!

Algebra Level 1

Find the minimum value of

x2+y2z+z2+x2y+y2+z2x, \frac { { x }^{ 2 }+{ y }^{ 2 } }{ z } +\frac { { z }^{ 2 }+{ x }^{ 2 } }{ y } +\frac { { y }^{ 2 }+{ z }^{ 2 } }{ x },

subject to x+y+z=2015 x + y + z = 2015 and x,y,z>0 x, y ,z > 0 .

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