KMO 2014 Problem 7

Let $x, y, z$ be the real numbers that satisfies the following. $(x-y)^2+(y-z)^2+(z-x)^2=8, x^3+y^3+z^3=1$ Find the minimum value of $x^4+y^4+z^4$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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