SMO selected Problem

Algebra Level 4

Let \[x_{1},x_{2},x_{3}\] be positive real number.Find the maximum of: \[\frac{(x_{1}^{2}+x_{2}^{2}+x_{3}^{2})^{3}}{(x_{1}^{3}+x_{2}^{3}+x_{3}^{3})^{2}}\]

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