RMO Practice problem 11

Algebra Level 3

Find the minimum value of x2+y2z+y2+z2x+x2+z2y\frac{x^{2}+y^{2}}{z}+\frac{y^{2}+z^{2}}{x}+\frac{x^{2}+z^{2}}{y} subject to x+y+z=1012x+y+z=1012 and x,y,z>0x,y,z>0.

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