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let a, b , c are distinct integers and w (omega) and w^2 are imaginary cube root of unity . then minimum value of / a+bw +c(w)^2 / + / a+b (w)^2+cw /.

let a, b , c are distinct integers and w (omega) and w^2 are imaginary cube root of unity . then    minimum value of  


/ a+bw +c(w)^2 / + /  a+b (w)^2+cw /.

Grade:12

3 Answers

pratish shrivastava
31 Points
11 years ago
/a+bw+cw^2/+a+b(w)^2+cw=/2a+b(w+(w)^2)+c(w+(w)^2)=/2a-b-c/
jagdish singh singh
173 Points
11 years ago

Nikhil verma
13 Points
2 years ago
We habe to find the value of k=|a+bw+cw2|
Here a,b,c are consecutive integer 
 
So lets take a=n-1 ,b=n ,c=n+1
K=|n-1+n(w)+(n+1)(w2))|
 =|n-1+nw+nw2+w2|
 =|n(1+w+w2)+w2-1|
         [1+w+w2=0]
 =|w2-1|
 =|(-1-√3i)/2-1|
=|(-3-√3i)/2|
=√{(3/2)2+(√3/2)2}
=√(9/4)+(3/4)
=√12/4
=√3

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