6. gt ⇔1ab+1bc+1ca+1a+1b+1c=6 $3(\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}})+3\geq 2(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}+\frac{1}{a} +\frac{1}{b}+\frac{1}{c})=12\Rightarrow \frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}\geq3dấu "=" \Leftrightarrow a=b=c=1$
6. gt \Leftrightarrow \frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=6 $3(\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}})+3\geq 2(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}+\frac{1}{a}+\frac{1}{b}+\frac{1}{c} )=12 \Rightarrow \frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}} \geq 3dấu "=" \Leftrightarrow a=b=c=1$
6. gt
\Leftrightarrow \frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=6 $3(\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}})+3\geq 2(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}+\frac{1}{a}
+\frac{1}{b}+\frac{1}{c})=12
\Rightarrow \frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}\geq3
dấu "=" \Leftrightarrow a=b=c=1$