JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The least value of the product \(xyz\) for which the determinant \(\left| {\begin{array}{*{20}{c}}
x&1&1 \\
1&y&1 \\
1&1&z
\end{array}} \right|\) is non-negative, is
- A \(-2\sqrt 2\)
- B \(-1\)
- C \(-16\sqrt 2\)
- D \(-8\)
Answer & Solution
Correct Answer
(D) \(-8\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{*{20}{c}} x&1&1\\ 1&y&1\\ 1&1&z \end{array} \ge 0\) \(xyz - x - y - z + 2 \ge 0\) \(xyz + 2 \ge x + y + z \ge 3{\left( {xyz} \right)^{1/3}}\) \(xyz + 2 - 3{\left( {xyz} \right)^{1/3}} \ge 0\) at \(\left( {xyz} \right) = {t^3}\) \({t^3} - 3t + 2 \ge 0\)…
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