11use the triangular inequality
|a+bω+cω2|≤|a|+|bω|+|cω2|
now it could be done by much easier method
put a=0,b=0,c=1
or
a=1,b=0,c=0
or
a=0,b=1,c=0
u will get ur answer
if a,b,c are integers not all simultaneously equal then the min value of l a + bω + cω2l is (where ω is cube root of unity).
ans. 1.
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11
1a b c can be any integers so how can we say tat putting 0,0,1 will give us min value...??
11agar not all simultaneously equal nahin likha hota then u could put a=0,b=0,c=0[1]
so u obtain min value as 0 in that case
1u must use the expansion
a3+b3+c3-3abc=(a+b+c)(a+bw+cw2)(a+bw2+cw)
u will get it...