Q.

If a, b, c are integers not all simultaneously equal then the minimum value of a++2 is (where ω is the cube root of unity 1)

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a

1

b

0

c

12

d

32

answer is D.

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Detailed Solution

a+bw+cw22=(a+bw+w2) (a+bw+cw2) =a2+b2+c2-ab-bc-ca =12a-b2+(b-c)2+(c-a)2>0

a, b, c are integers not all equal min value =1

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