A) Cannot be less than 1
B) Is greater than \[-8\]
C) Is less than \[-8\]
D) Must be greater than 8
Correct Answer: B
Solution :
[b] \[\left| \begin{matrix} a & 1 & 1 \\ 1 & b & 1 \\ 1 & 1 & c \\ \end{matrix} \right|>0\] \[\Rightarrow \,\,\,\,a(bc-1)-1(c-1)+1(1-b)>0\] \[\Rightarrow \,\,\,\,abc-a-c+1+1-b>0\] \[\Rightarrow \,\,\,\,abc+2-(a+b+c)>0\] \[\Rightarrow \,\,\,\,abc>(a+b+c)-2\] Let; \[a=-1;\] \[b=0\] & \[c=1\] Then; \[0>-2\] [which is correct] Hence, \[abc=0\Rightarrow abc>-8\]You need to login to perform this action.
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