Q = $2a^{2} +2b^{2} - \frac{6a}{b} - \frac{6b}{a} +\frac{9}{a^{2}} +\frac{9}{b^{2}}$ $=( a^{2} -\frac{6a}{b} +\frac{9}{b^{2}} )+ (b^{2} -\frac{6b}{a} +\frac{9}{a^{2}} ) +a^{2} +b^{2}$ $ =(a-\frac{3}{b})^{2} +(b -\frac{3}{a} )^{2} +a^{2} +b^{2}$ $ \geq 2(a-\frac{3}{b} )(b-\frac{3}{a} ) +a^{2} +b^{2}$ =$2(ab -3 -3 +\frac{9}{ab} ) +(a +b)^{2} -2ab$$\Rightarrow Q\geq 2(ab -6 +\frac{9}{ab} )+4-2ab=-12 +4+\frac{18}{ab}$ $(a+b)^{2} \geq 4ab \Rightarrow ab\leq 1 \Rightarrow \frac{18}{ab} \geq 18 $ $ \Rightarrow Q \geq 10$ dấu ''=''$ \Leftrightarrow a=b=1$
Q = $2a^{2}$ +$2b^{2}$ - $\frac{6a}{b}$ - $\frac{6b}{a}$ +$\frac{9}{a^{2}}$ +$\frac{9}{b^{2}}$ =( $a^{2} $-$\frac{6a}{b}$ +$\frac{9}{b^{2}}$ )+ ($b^{2}$ -$\frac{6b}{a}$+$\frac{9}{a^{2}}$) +$a^{2}$+$b^{2}$ =$(a-\frac{3}{b})^{2}$ +$(b -\frac{3}{a} )^{2}$ +$a^{2}$ +$b^{2}$ $\geq 2(a-\frac{3}{b} )(b-\frac{3}{a} ) + $a^{2}$ + $b^{2}$ =2(ab -3 -3 +$\frac{9}{ab}$ ) +$(a +b)^{2}$ -2ab$\Rightarrow$ Q $\geq$ 2(ab -6 +$\frac{9}{ab}$ )+4-2ab=-12 +4+$\frac{18}{ab}$ $(a+b)^{2}$ $\geq$ 4ab $\Rightarrow$ ab $\leq$ 1 $\Rightarrow$ $\frac{18}{ab}$ $\geq$ 18 $\Rightarrow$ Q $\geq$ 10 dấu ''='' $\Leftrightarrow$ a=b=1
Q = $2a^{2} +2b^{2} - \frac{6a}{b} - \frac{6b}{a} +\frac{9}{a^{2}} +\frac{9}{b^{2}}$
$=( a^{2} -\frac{6a}{b} +\frac{9}{b^{2}} )+ (b^{2} -\frac{6b}{a}
+\frac{9}{a^{2}}
) +a^{2}
+b^{2}$
$ =(a-\frac{3}{b})^{2} +(b -\frac{3}{a} )^{2} +a^{2} +b^{2}$ $
\geq 2(a-\frac{3}{b} )(b-\frac{3}{a} ) +a^{2} +b^{2}$ =
$2(ab -3 -3 +\frac{9}{ab} ) +(a +b)^{2} -2ab
$$\Rightarrow Q\geq 2(ab -6 +\frac{9}{ab} )+4-2ab=-12 +4+\frac{18}{ab}$ $(a+b)^{2} \geq 4ab \Rightarrow ab\leq 1 \Rightarrow \frac{18}{ab} \geq 18
$ $
\Rightarrow Q \geq 10
$ dấu ''=''$
\Leftrightarrow a=b=1
$