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Question

Given that a, b and c are positive real numbers, such that a+b+c= x, then which of the following is true?

A
(x-a)(x-b)(x-c)≥8abc
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B
1/a + 1/b + 1/c ≥ 9/x
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C
(x-a)(x-b)(x-c)≥8/27a3
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D
a,b and c
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Solution

The correct option is D a,b and c

Assumption of values is the easiest way to solve. a=b=c=1 and x=3.

Take a=1, b=2 and c=3. x=6. all 3 still hold good. Answer option d.

Note: with answer options like “All of these” and “None of these” you need to be a bit careful. Do not mark the answer based on only one set of values. Take two cases and see which options fit in BOTH the cases.


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