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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    Best answer

    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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