GAIC Math 2024 Problem 75

Set $x, y, z$ are real numbers, satisfying $x^{2}+y^{2}+z^{2}=1$ . Then the maximum and minimum of $(x-y)(y-z)(x-z)$ are

Dataset text MathOdyssey. Open licence.

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$\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}$

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