The least value of the product \( x y z \) for which the \( \left|\...

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The least value of the product \( x y z \) for which the \( \left|\begin{array}{lll}x & 1 & 1 \\ 1 & y & 1 \\ 1 & 1 & z\end{array}\right| \) is non-negative is:
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