1) < 3 / 2
2) ≥ 3 / 2
3) > 5 / 2
4) none of these
Solution: (2) ≥ 3 / 2
AM of (- 1)th powers ≥ (- 1)th powers of AM
[(b + c) / (a + b + c)]-1 + [(c + a) / (a + b + c)]-1 + [(a + b) / (a + b + c)]-1 > {[(b + c) / (a + b + c) + (c + a) / (a + b + c) + (a + b) / (a + b + c)] / 3}-1 — (2) [(a + b + c) / (b + c) + (a + b + c) / (c + a) + (a + b + c) / (a + b)] ≥ (2 / 3)-1a / (b + c) + 1 + b / (c + a) + 1 + c / (a + b) ≥ 3 * (3 / 2)
a / (b + c) + b / (c + a) + c / (a + b) ≥ (9 / 2) – 3 = 3 / 2
a / (b + c) + b / (c + a) + c / (a + b) ≥ 3 / 2
