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If a + b + c = 0, then the value of [(a + b)/c + (b + c)/a + (c + a)/b] x [a/(b + c) + b/(c + a) + c/(a + b)] is ?
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- 9
- 0
- 8
- -3
Correct Option: A
Since, a + b + c = 0
Then, a + b = -c ....(i)
a + c = -b .........(ii)
b + c = -a ....(iii)
Now, [(a + b)/c + (b + c)/a + (c + a)/b] x [a/(b + c) + b/(c + a) + c/(a + b)]
Now, putting the value of a + b , b + c and c + a from Eqs. (i), (ii) and (iii) , we get
[(-c)/c + (-a)/a + (-b)/b] x [a/-a + b/-b + c/-c]
[(-1) + (-1) + (-1)] [(-1) + (-1) + (-1)]
= (-3) x (-3) = 9
