RMO Practice problem 11

Algebra Level 4

Find the minimum value of \[\frac{x^{2}+y^{2}}{z}+\frac{y^{2}+z^{2}}{x}+\frac{x^{2}+z^{2}}{y}\] subject to \(x+y+z=1012\) and \(x,y,z>0\).

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