Cube root of unity

If w ( â‰ 1) is cube root of unity satisfying 1/a+w + 1/b+w + 1/c+w = 2w²

and ,1/a+w² + 1/b+w² + 1/c+w² = 2w

then the value of 1/a+1 + 1/b+1 + 1/c+1 is ?

ans 2

5 Answers

1, w and w² be the roots of the equation
1a+x + 1b+x + 1c+x = 2x

how?

i am also trying to figure out why /..
btw it should be
1a+x+1b+x+1b+x=2x²

http://www.artofproblemsolving.com/Forum/viewtopic.php?f=151&t=407351&p=2275357#p2275357

yup.. i commited a mistake there.. right hand side would have been 2x

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