Problem

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Tags: inequalities, calculus, derivative, Cauchy Inequality, inequalities proposed



Let $ x,y,z$ be positive real numbers,satisfying equality $ x^{2}+y^{2}+z^{2}=25$. Find the minimal possible value of the expression $ \frac{xy}{z} + \frac{yz}{x} + \frac{zx}{y}$.