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Q.

If a=20C0+20C3+20C6+20C9+…;b=20C1+20C4+20C7+…; and c=20C2+20C5+20C8+…, thenValue of a3+b3+c3-3abc isValue of (a−b)2+(b−c)2+(c−a)2 is

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a

210

b

220

c

0

d

219

e

1

f

2

g

220

h

240

answer is , .

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Detailed Solution

We have                    a+b+c=220Now, a3+b3+c3−3abc        =(a+b+c)a+bω+cω2a+bω2+cω        =220(1+ω)201+ω220        =220(a−b)2+(b−c)2+(c−a)2 =2a+bω+cω2a+bω2+cω =2
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If a=20C0+20C3+20C6+20C9+…;b=20C1+20C4+20C7+…; and c=20C2+20C5+20C8+…, thenValue of a3+b3+c3-3abc isValue of (a−b)2+(b−c)2+(c−a)2 is