Advance Happy New Year 2015!

Algebra Level 2

Find the minimum value of

\[ \frac { { x }^{ 2 }+{ y }^{ 2 } }{ z } +\frac { { z }^{ 2 }+{ x }^{ 2 } }{ y } +\frac { { y }^{ 2 }+{ z }^{ 2 } }{ x }, \]

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

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