2. Q≤12a2b+2ab2+12ab2+2a2b=1ab(a+b)1a+1b=2⇒a+b=2ab ⇒Q≤12a2b2(a+b)2≥4ab⇔(a+b)2≥2(a+b)⇔a+b≥2 ⇔a+bab≥2ab⇔2≥2ab $\Rightarrow ab \geq1$$\Rightarrow Q \leq \frac{1}{2} dấu "=" \Leftrightarrow a=b=1$
2. Q \leq \frac{1}{2a^{2}b+2ab^{2}}+\frac{1}{2ab^{2}+2a^{2}b}=\frac{1}{ab(a+b)}\frac{1}{a}+\frac{1}{b}=2 \Rightarrow a+b=2ab \Rightarrow Q\leq \frac{1}{2a^{2}b^{2}}(a+b)^{2}\geq 4ab \Leftrightarrow (a+b)^{2}\geq2(a+b) \Leftrightarrow a+b\geq2 \Leftrightarrow \frac{a+b}{ab}\geq \frac{2}{ab} \Leftrightarrow 2\geq \frac{2}{ab} $\Rightarrow ab\leq 1 \Rightarrow Q\leq \frac{1}{2} dấu "=" \Leftrightarrow a=b=1$
2.
Q \leq \frac{1}{2a^{2}b+2ab^{2}}+\frac{1}{2ab^{2}+2a^{2}b}=\frac{1}{ab(a+b)}\frac{1}{a}+\frac{1}{b}=2 \Rightarrow a+b=2ab \Rightarrow Q\leq \frac{1}{2a^{2}b^{2}}(a+b)^{2}\geq 4ab \Leftrightarrow (a+b)^{2}\geq2(a+b) \Leftrightarrow a+b\geq2 \Leftrightarrow \frac{a+b}{ab}\geq \frac{2}{ab} \Leftrightarrow 2\geq \frac{2}{ab} $\Rightarrow ab
\
geq1
$$\Rightarrow Q
\leq \frac{1}{2}
dấu "=" \Leftrightarrow a=b=1$