Find The Value of [(a + b)/c + (b + c)/a + (c + a)/b] [a/(b + c) + b/(c + a) + c/(a + b)] : If

If a + b + c = 0, then the value of [(a + b)/c + (b + c)/a + (c + a)/b] [a/(b + c)  + b/(c + a) + c/(a + b)] is

  1. 9
  2. 0
  3. 8
  4. -3
Anurag Mishra Professor Asked on 1st August 2015 in Maths.
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Answer:  (1)  9
Explanation:-
 Given-
a + b + c = 0
Then, a + b = – c ……………………. (1)
a + c = – b …………………………… (2)
b + c = -a ………………………………. (3)
Now,
[(a + b)/c + (b + c)/a + (c  + a)/b] [a/(b + c) + b/(c + a) + c/(a + b)]
Put the value of a + b, b + c, c + a  from equation (1), (2) & (3)
=[(-c)/c + (-a)/a + (-b)/b] = [a/(-a) + b/(-b) + c/(-c)]
=[(-1) + (-1) + (-1)] [(-1) + (-1) + (-1) ]
=(- 1 – 1 – 1) (-1 – 1 – 1)
= (-3) (-3)
= 9
Hence, the answer is (1) 9.

Anurag Mishra Professor Answered on 1st August 2015.
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