6. gt $\Leftrightarrow \frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=6$ $3(\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}})+3\geq 2(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}+\frac{1}{a} +\frac{1}{b}+\frac{1}{c})=12$ $\Rightarrow \frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}\geq3$dấu "=" $\Leftrightarrow a=b=c=1$
6. gt $\Leftrightarrow \frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=6$ $3(\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}})+3\geq 2(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}+\frac{1}{a}+\frac{1}{b}+\frac{1}{c} )=12$ $\Rightarrow \frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}} \geq 3$dấu "=" $\Leftrightarrow a=b=c=1$
6. gt $\Leftrightarrow \frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=6$ $3(\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}})+3\geq 2(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}+\frac{1}{a}
+\frac{1}{b}+\frac{1}{c})=12$ $\Rightarrow \frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}\geq3$dấu "=" $\Leftrightarrow a=b=c=1$