Question

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

• A. $-8$
• B. $-1$
• C. $-2\sqrt{2}$
• D. $-16\sqrt{2}$
• E. None of these

Answer 1

The correct option is E None of these

Insufficient Data.
If we take $y=z=1,$ the value of determinant become $0,\forall x\in R.$
$\Rightarrow$ the value of $xyz$ has no lower bound