X cube + 1 by x cube minus 2 is equal to zero
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Answer:
Since, a,b and c satisfies
[
a
b
c
]
⎣
⎢
⎢
⎡
1
8
7
9
2
3
7
7
7
⎦
⎥
⎥
⎤
=[
0
0
0
]
So, we get the equations
a+8b+7c=0
9a+2b+3c=0
7a+7b+7c=0 or a+b+c=0
Since , a=2, so the equations become
2+8b+7c=0 .....(1)
18+2b+3c=0 .....(2)
2+b+c=0 .....(3)
Solving above equations, we get b=12,c=−14
ω
a
3
+
ω
b
1
+
ω
c
3
=
ω
2
3
+
ω
12
1
+
ω
−14
3
=
ω
2
3
+
ω
12
1
+3ω
14
=
ω
2
3
+
(ω
3
)
4
1
+3(ω
3
)
4
ω
2
=3ω+1+3ω
2
=3(ω+ω
2
)+1
Since 1+ω+ω
2
=0,
So,
ω
a
3
+
ω
b
1
+
ω
c
3
=3(−1)+1=−2
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