Ta cần chứng minh:
\(\sqrt{\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}}=\left|\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\right|\)
\(\Leftrightarrow\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}=\left|\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\right|^2\)
\(\Leftrightarrow\dfrac{2}{ab}+\dfrac{2}{bc}+\dfrac{2}{ca}=0\)
\(\Leftrightarrow\dfrac{a+b+c}{abc}=0\)(đúng)