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
• B. 1/a + 1/b + 1/c ≥ 9/x
• C. (x-a)(x-b)(x-c)≥8/27a³
• D. a,b and c
• E. None of a, b and c

Answer 1

The correct option is D a,b and c

option (d)

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.