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$