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Let a,b and c be three real numbers sa...

Let a,b and c be three real numbers satisfying
[a b c ] `|(1,9,7),(8,2,7),(7,3,7)|`=[ 0 0 0 ] ….(i)
Let `omega` be a solution of `x^3-1=0` with `lim(omega) > 0` . If a=2 with b and c satisfying Eq.(i) then the value of `3/omega^4+ 1/omega^b + 1/omega^c` is :

A

0

B

12

C

7

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
We have
`[(a,b,c)][(1,9,7),(8,2,7),(7,3,7)]=[(0,0,0)]`
`implies a+8b+7c=0,9a+2b+3c=0,7a+7b+7c=0`
`impliesa=1,b=6,c=-7`
Clearly `P(a,b,c)` lies on the plane `2x+y+z=1`
`:.7a+b+c=7+6-7=6`
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