Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

If a, b, c are +ve real numbers, then a / (b + c) + b / (c + a) + c / (a + b) is

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)-1

a / (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

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