KURSCHAK 1964 Problem 3

Show that for any positive reals $w, x, y, z$ we have $\sqrt{\frac{w^2 + x^2 + y^2 + z^2}{4}}\ge \sqrt[3]{ \frac{wxy + wxz + wyz + xyz}{4}}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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