solve the following by wavy curve method (plz don't spam or else I will report plz reply quick )
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Answer:
x
2
+x+1=0 implies
x=w,w
2
where w,w
2
are cube roots of unity.
Now
1+w+w
2
=0
w
3
=1
And
w
ˉ
=w
2
.
Now
(x+
x
1
)
2
+(x
2
+
x
2
1
)
2
....(x
27
+
x
27
1
)
2
=(w+
w
ˉ
)
2
+(w
2
+
w
2
ˉ
)
2
+...(w
27
+
w
27
ˉ
)
2
=(w+w
2
)
2
+(w
2
+w)
2
+(2)
2
+(w+w
2
)
2
+...(2)
2
=9(2
2
)+18(w+w
2
)
2
=36+18(−1)
2
=36+18
=54
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