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If the system a(y + z) = x, b(z + x) = y, c(x + y) = z (with a, b, c not equal to -1) has a nontrivial solution, find the value of 1/(1 + a) + 1/(1 + b) + 1/(1 + c).

1. 0
2. 1
3. 2
4. 3

Correct answer: 2

Solution

From a(x+y+z) = (1+a)x etc., we get x = a*s/(1+a), and summing x+y+z = s forces a/(1+a) + b/(1+b) + c/(1+c) = 1, which converts to the required sum equal to 2.

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