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

If a, b, c are positive numbers, then least value of (a + b + c)(1/a + 1/b + 1/c) is

(a) 1 

(b) 6 

(c) 9 

(d) None

Solution:

We use A.M ≥ H.M

(a+b+c)/3 ≥ 3/[(1/a) + (1/b) + (1/c)]

=> (a + b + c)(1/a + 1/b + 1/c) ≥ 9

The least value of (a + b + c)(1/a + 1/b + 1/c) is 9.

Hence option c is the answer.

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