Not \(x = y = z\)

Algebra Level 5

\[\large\dfrac{x^3+y^3+z^3}{(x+y+z)(x^2+y^2+z^2)}\]

Let \(x, y, z\) be non-negative real numbers such that \(x^2+y^2+z^2=2(xy+yz+zx)\). Find the maximum value of the expression above.

Give your answer to 3 decimal places.

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