Vì \(\left(x^2-9\right)^2\ge0\)\(\forall x\inℝ\); \(\left|y-2\right|\ge0\)\(\forall y\inℝ\)
\(\Rightarrow\left(x^2-9\right)^2+\left|y-2\right|\text{}\ge0\)\(\forall x,y\inℝ\)\(\Rightarrow\)\(\left(x^2-9\right)^2+\left|y-2\right|\text{}+10\ge10\)\(\forall x,y\inℝ\)
Dấu " = " xảy ra \(\Leftrightarrow\hept{\begin{cases}x^2-9=0\\y-2=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x^2=9\\y=2\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\pm3\\y=2\end{cases}}\).
Vậy GTNN Q = 10 khi y = 2 và x = ±3
