1okie :)
if a,b,c \epsilon R satisfy
1a + 1b + 1c =1a+b+c
find the value of
( 1/a +1/b + 1/c)2007 - 2007a2007 +b2007 +c2007 +2006(a+b+c)2007
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4 Answers
62This was a very very recent question of the day..
The answer is a=-b or a=-c or b=-c
using which we can say that
the given expressoin is
1/a2007 - 2007/a2007+2006/a2007 = 0
1ok thks..........i suppose all questions which i hav asked hav already been asked befor[3]
62my wrong.. this was not solved very recently
that was a slightly different question
http://targetiit.com/iit-jee-forum/posts/solve-this-set-of-equations-11666.html
I was talking about this one.. (This has not been solved yet!)
So the justification for my first step :
1/a+1/b+1/c = 1/(a+b+c)
1/b+1/c = 1/(a+b+c)-1/a
1/b+1/c = a-a-b-ca(a+b+c)
(b+c)/bc = -b-ca(a+b+c)
(b+c)/bc = -b+ca(a+b+c)
(b+c)/bc+b+ca(a+b+c) = 0
(b+c){1bc+1a(a+b+c)} = 0
Which on a couple more steps that i leave for you as an exercise will give you that either (b+c) is zero or (a+b) is zero or (a+c) is zero..
Then continue to read my previous post.