Đáp án:
Giải thích các bước giải:
Ta có:
\[\begin{array}{l}
{\left( {\frac{1}{a} + \frac{1}{b} + \frac{1}{c}} \right)^2} = \frac{1}{{{a^2}}} + \frac{1}{{{b^2}}} + \frac{1}{{{c^2}}} + 2\left( {\frac{1}{{ab}} + \frac{1}{{bc}} + \frac{1}{{ca}}} \right)\\
= \frac{1}{{{a^2}}} + \frac{1}{{{b^2}}} + \frac{1}{{{c^2}}} + 2.\frac{{a + b + c}}{{abc}} = \frac{1}{{{a^2}}} + \frac{1}{{{b^2}}} + \frac{1}{{{c^2}}}
\end{array}\]