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Question

Ifa,bandc are different positive real numbers ,then [a+b+c]1a+1b+1c is


A

<9

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B

>9

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C

>0

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D

>24

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Solution

The correct option is B

>9


Explanation for the correct option:

Applying AM-GM inequality:

[a+b+c]1a+1b+1c

AM>GM

[a+b+c]3>(abc)13

[a+b+c]>3(abc)13 — (1)

Similarly, 1a+1b+1c3>1a1b1c13

1a+1b+1c>31abc13 — (2)

Multiply equation (1) and (2),

[a+b+c]1a+1b+1c>9

Hence, option ‘B’ is correct.


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