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