Algebra

Blazing goIITian

Joined: 21 Mar 2012
Post: 1457
31 Mar 2012 01:03:43 IST
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complex no.
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

if we are given that  1/(a+w) + 1/(b+w) +1/(c+w) ==2w2 also 1/(a+w2) + 1/(b+w2) + 1/(c+w2) ==2w thennnn............1/(a+1) + 1/(b+1) + 1/(c+1) ==????????? ur options are a)2 b)-2 c)-1+w d)cant bee determined...................



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Blazing goIITian

Joined: 21 Mar 2012
Posts: 1457
31 Mar 2012 01:07:02 IST
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Where w is complex cube root of unity
prahlad kumar sharma's Avatar

Cool goIITian

Joined: 21 Jul 2010
Posts: 88
31 Mar 2012 09:29:07 IST
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its 2.
simplifly the two equations and get abc=1/2 and ab+bc+ca=0

hemang's Avatar

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
31 Mar 2012 11:00:32 IST
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w and w^2 are the roots of

1/(a + x^2) + 1/( b + x^2) + 1/(c + x^2) = 2x.

put x = 1, get RHS = 2.

:)

 




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