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

Let a, b, and c be three real numbers satifying `[(a, b, c)]`
`[(1,9,7),(8,2,7),(7,3,7)]=[(0,0,0)]`
Let `omega` be a solution of `x^(3)-1=0` with `Im (omega) gt 0`. If `a=2` with b and c satisfying (E), then the value of `3/omega^(a)+1/omega^(b)+3/omega^(c)` is equal to

A

`-2`

B

2

C

3

D

`-3`

Text Solution

Verified by Experts

The correct Answer is:
A
If a = 2, b= 12, c=-14
`therefore (3)/(omega^(a)) + (1)/(omega^(b)) + (3)/(omega^(c))`
`rArr (3)/(omega^(2)) + (1)/(omega^(12)) + (3)/(omega^(-14)) = (3)/(omega^(2)) + 1 + 3omega^(2) = 3omega + 1 +3omega^(2)`
` = 1+ 3 (omega + omega^(2)) = 1-3 =-2`
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