Ta có: pt $\Leftrightarrow \sqrt{(x-\frac{3\sqrt{2}}{2})^2+\frac{9}{2}}+\sqrt{(x-2\sqrt{2})^2+8}=5$Trong Oxy, xét 2 vecto $\overrightarrow{u}=(x-\frac{3\sqrt{2}}{2};\frac{3\sqrt{2}}{2}),\overrightarrow{v}(2\sqrt{2}-x;2\sqrt{2})$
Suy ra: $\left\{ \begin{array}{l} /\overrightarrow{u}/=.......\\ /\overrightarrow{v}/=....... \end{array} \right.\Rightarrow \left\{ \begin{array}{l} \overrightarrow{u}+\overrightarrow{v}=.....\\ /\overrightarrow{u}+\overrightarrow{v}/=.......=5 \end{array} \right.$
Mà ta luôn có: $/\overrightarrow{u}/+/\overrightarrow{v}/\geq /\overrightarrow{u}+\overrightarrow{v}|$
$\Leftrightarrow ........\Rightarrow VT\geq VP.$
$\rightarrow .............$
Đẳng thức khi: $\frac{x-\frac{3\sqrt{2}}{2}}{2\sqrt{2}-x}=\frac{3}{4}\rightarrow ............$