Find the value of (1-x+x²)(1+x-x²) = ?
Where x is the cube root of unity.
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Answer:
(x+2)
2
=(ω−ω
2
)
x
2
+4x+4=ω
2
+ω
4
−2ω
3
=ω
2
+ω−2
As ω
2
+ω+1=0
ω
2
+ω=−1
ω
3
=1
x
2
+4x+4=−1−2=−3
x
2
+4x+7=0
Now, by long division method, we can say that
x
4
+3x
3
+2x
2
−11x−6=(x
2
+4x+7)(x
2
−x−1)+1
As x=ω−ω
2
−2
x
2
+4x+7=0
Therefore value of
x
4
+3x
3
+2x
2
−11x−6 is 1
December 26, 2019
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