question_answer

Let \[{{a}_{1}},\] \[{{a}_{2}},\] \[{{a}_{3}}\] be any positive real numbers, then which of the following statement is true?

A)  \[({{a}_{1}}+{{a}_{2}}+{{a}_{3}})\,\,\left( \frac{1}{{{a}_{1}}}+\frac{1}{{{a}_{2}}}+\frac{1}{{{a}_{3}}} \right)\ge 9\]

B)  \[3\,{{a}_{1}}{{a}_{2}}{{a}_{3}}\le a_{1}^{3}+a_{2}^{3}+a_{3}^{3}\]

C)  \[({{a}_{1}}+{{a}_{2}}+{{a}_{3}})\,\,{{\left( \frac{1}{{{a}_{1}}}+\frac{1}{{{a}_{2}}}+\frac{1}{{{a}_{3}}} \right)}^{3}}\ge 27\]

D)  All of these

E)  None of these