\( x=1, y-c,-5 \quad\left|\begin{array}{lll}a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c\end{array}\right| \) is positive then
\( x=1, y-c,-5 \quad\left|\begin{array}{lll}a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c\end{array}\right| \) is positive then
(a) \( a b c>-11 \)
(b) \( a b c<-8 \)
(c) \( a b c>-8 \)
(d) None of these
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\(\begin{vmatrix}a&1&1\\1&b&1\\1&1&c\end{vmatrix}>0\)
⇒ a\(\begin{vmatrix}b&1\\1&c\end{vmatrix}-1\begin{vmatrix}b&1\\1&c\end{vmatrix}\) + \(1\begin{vmatrix}1&b\\1&1\end{vmatrix}>0\)
⇒ a(bc - 1) - 1(c - 1) + 1(1 - b) > 0
⇒ abc - a - c + 1+ 1 - b >0
⇒ abc - (a + b + c) + 2 >0
⇒ abc >(a + b + c) - 2
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