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Question

IF ω is a cube root of unity but not equal to 1 then minimum value of a+bw+cw2 (where a ,b, c are integers but not all equal) is

A
0
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B
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C
1
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D
2
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Solution

The correct option is C 1

Let y= a+bw+cw2

for y to be minimum y2 must be minimum.

y2= a+bw+cw22

y2=(a+bw+cw2)(a+bw+cw2)

=12[(ab)2+(bc)2+(ca)2]

Since a,b and c are not equal at a time so minimum value of y2 occurs when any
two are same and third is differ by 1.

Minimum of y=1 (as a,b,c are integers)


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