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	3	thêm 175 ký tự trong đáp án		Sửa 11-03-13 01:05 PM gunbk92 1
a/$3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}$ =$3\overrightarrow{OA}+\overrightarrow{OG}+\overrightarrow{GB}+\overrightarrow{OG}+\overrightarrow{GC}+\overrightarrow{OG}+\overrightarrow{GD}$ =$3(\overrightarrow{OA}+\overrightarrow{OG})+(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})=0$(đpcm)b/$3MA^2+MB^2+MC^2+MD^2$$=3(\overrightarrow{MO}+\overrightarrow{OA})^2+(\overrightarrow{MO}+\overrightarrow{OB})^2+(\overrightarrow{MO}+\overrightarrow{OC})^2+(\overrightarrow{MO}+\overrightarrow{OD})^2$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2+2\overrightarrow{MO}(3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD})$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2$ (đpcm)c/ $k^2=3MA^2+MB^2+MC^2+MD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+OB^2+OC^2+OD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+(\overrightarrow{OG}+\overrightarrow{GB})^2+(\overrightarrow{OG}+\overrightarrow{GC})^2+(\overrightarrow{OG}+\overrightarrow{GD})^2$ $\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2+2\overrightarrow{OG}(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})$$\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2$ $\begin{cases}\overrightarrow{OA}=\frac{1}{2}\overrightarrow{GA} \\ \overrightarrow{OG}=\frac{1}{2}\overrightarrow{AG} \end{cases}$$\Rightarrow k^2=6MO^2+\frac{3}{2}AG^2$$\Leftrightarrow MO^2=\frac{1}{6}(k^2-\frac{3}{2}AG^2)$ $+k^2<3/2AG^2 $ Quỹ tích M thuộc rỗng $+k^2=3/2AG^2$ Quỹ tích M là O$+k^2>3/2AG^2$ Quỹ tích M là đường tròn tâm 0, bán kính R=$\sqrt{\frac{1}{6}(k^2-\frac{3}{2}AG^2)}$ a/$3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}$ =$3\overrightarrow{OA}+\overrightarrow{OG}+\overrightarrow{GB}+\overrightarrow{OG}+\overrightarrow{GC}+\overrightarrow{OG}+\overrightarrow{GD}$ =$3(\overrightarrow{OA}+\overrightarrow{OG})+(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})=0$(đpcm)b/$3MA^2+MB^2+MC^2+MD^2$$=3(\overrightarrow{MO}+\overrightarrow{OA})^2+(\overrightarrow{MO}+\overrightarrow{OB})^2+(\overrightarrow{MO}+\overrightarrow{OC})^2+(\overrightarrow{MO}+\overrightarrow{OD})^2$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2+2\overrightarrow{MO}(3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD})$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2$ (đpcm)c/ $k^2=3MA^2+MB^2+MC^2+MD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+OB^2+OC^2+OD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+(\overrightarrow{OG}+\overrightarrow{GB})^2+(\overrightarrow{OG}+\overrightarrow{GC})^2+(\overrightarrow{OG}+\overrightarrow{GD})^2$ $\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2+2\overrightarrow{OG}(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})$$\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2$ $\begin{cases}\overrightarrow{OA}=\frac{1}{2}\overrightarrow{GA} \\ \overrightarrow{OG}=\frac{1}{2}\overrightarrow{AG} \end{cases}$$\Rightarrow k^2=6MO^2+\frac{3}{2}AG^2$$\Leftrightarrow MO^2=\frac{1}{6}(k^2-\frac{3}{2}AG^2)$ a/$3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}$ =$3\overrightarrow{OA}+\overrightarrow{OG}+\overrightarrow{GB}+\overrightarrow{OG}+\overrightarrow{GC}+\overrightarrow{OG}+\overrightarrow{GD}$ =$3(\overrightarrow{OA}+\overrightarrow{OG})+(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})=0$(đpcm)b/$3MA^2+MB^2+MC^2+MD^2$$=3(\overrightarrow{MO}+\overrightarrow{OA})^2+(\overrightarrow{MO}+\overrightarrow{OB})^2+(\overrightarrow{MO}+\overrightarrow{OC})^2+(\overrightarrow{MO}+\overrightarrow{OD})^2$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2+2\overrightarrow{MO}(3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD})$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2$ (đpcm)c/ $k^2=3MA^2+MB^2+MC^2+MD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+OB^2+OC^2+OD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+(\overrightarrow{OG}+\overrightarrow{GB})^2+(\overrightarrow{OG}+\overrightarrow{GC})^2+(\overrightarrow{OG}+\overrightarrow{GD})^2$ $\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2+2\overrightarrow{OG}(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})$$\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2$ $\begin{cases}\overrightarrow{OA}=\frac{1}{2}\overrightarrow{GA} \\ \overrightarrow{OG}=\frac{1}{2}\overrightarrow{AG} \end{cases}$$\Rightarrow k^2=6MO^2+\frac{3}{2}AG^2$$\Leftrightarrow MO^2=\frac{1}{6}(k^2-\frac{3}{2}AG^2)$ $+k^2<3/2AG^2 $ Quỹ tích M thuộc rỗng $+k^2=3/2AG^2$ Quỹ tích M là O$+k^2>3/2AG^2$ Quỹ tích M là đường tròn tâm 0, bán kính R=$\sqrt{\frac{1}{6}(k^2-\frac{3}{2}AG^2)}$

	2	bớt 15 ký tự trong đáp án		Sửa 10-03-13 05:59 PM gunbk92 1
a/$3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}$ =$3\overrightarrow{OA}+\overrightarrow{OG}+\overrightarrow{GB}+\overrightarrow{OG}+\overrightarrow{GC}+\overrightarrow{OG}+\overrightarrow{GD}$ =$3(\overrightarrow{OA}+\overrightarrow{OG})+(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})=0$(đpcm)b/$3MA^2+MB^2+MC^2+MD^2$$=3(\overrightarrow{MO}+\overrightarrow{OA})^2+(\overrightarrow{MO}+\overrightarrow{OB})^2+(\overrightarrow{MO}+\overrightarrow{OC})^2+(\overrightarrow{MO}+\overrightarrow{OD})^2$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2+2\overrightarrow{MO}(3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD})$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2$ (đpcm)c/ $k^2=3MA^2+MB^2+MC^2+MD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+OB^2+OC^2+OD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+(\overrightarrow{OG}+\overrightarrow{GB})^2+(\overrightarrow{OG}+\overrightarrow{GC})^2+(\overrightarrow{OG}+\overrightarrow{GD})^2$ $\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2+2\overrightarrow{OG}(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})$$\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2$ $\begin{cases}\overrightarrow{OA}=\frac{1}{2}\overrightarrow{GA} \\ \overrightarrow{OG}=\frac{1}{2}\overrightarrow{AG} \end{cases}$$\Rightarrow k^2=6MO^2+\frac{3}{2}AG^2$$\Leftrightarrow MO^2=\frac{1}{6}(k^2-\frac{3}{2}AG^2)$ a/$3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}$ =$3\overrightarrow{OA}+\overrightarrow{OG}+\overrightarrow{GB}+\overrightarrow{OG}+\overrightarrow{GC}+\overrightarrow{OG}+\overrightarrow{GD}$ =$3(\overrightarrow{OA}+\overrightarrow{OG})+(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})=0$(đpcm)b/$3MA^2+MB^2+MC^2+MD^2$$=3(\overrightarrow{MO}+\overrightarrow{OA})^2+(\overrightarrow{MO}+\overrightarrow{OB})^2+(\overrightarrow{MO}+\overrightarrow{OC})^2+(\overrightarrow{MO}+\overrightarrow{OD})^2$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2+2\overrightarrow{MO}(3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD})$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2$ (đpcm)c/ $k^2=3MA^2+MB^2+MC^2+MD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+OB^2+OC^2+OD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+(\overrightarrow{OG}+\overrightarrow{GB})^2+(\overrightarrow{OG}+\overrightarrow{GC})^2+(\overrightarrow{OG}+\overrightarrow{GD})^2$ $\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2+2\overrightarrow{OG}(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})$$\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2$ $\begin{cases}\overrightarrow{OA}=\frac{1}{2}\overrightarrow{GA} \\ \overrightarrow{OG}=\frac{1}{2}\overrightarrow{AG} \end{cases}$$\Rightarrow k^2=6MO^2+\frac{3}{2}AG^2$$\Leftrightarrow \overrightarrow{MO}=\frac{1}{6}(k^2-\frac{3}{2}AG^2)$ a/$3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}$ =$3\overrightarrow{OA}+\overrightarrow{OG}+\overrightarrow{GB}+\overrightarrow{OG}+\overrightarrow{GC}+\overrightarrow{OG}+\overrightarrow{GD}$ =$3(\overrightarrow{OA}+\overrightarrow{OG})+(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})=0$(đpcm)b/$3MA^2+MB^2+MC^2+MD^2$$=3(\overrightarrow{MO}+\overrightarrow{OA})^2+(\overrightarrow{MO}+\overrightarrow{OB})^2+(\overrightarrow{MO}+\overrightarrow{OC})^2+(\overrightarrow{MO}+\overrightarrow{OD})^2$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2+2\overrightarrow{MO}(3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD})$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2$ (đpcm)c/ $k^2=3MA^2+MB^2+MC^2+MD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+OB^2+OC^2+OD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+(\overrightarrow{OG}+\overrightarrow{GB})^2+(\overrightarrow{OG}+\overrightarrow{GC})^2+(\overrightarrow{OG}+\overrightarrow{GD})^2$ $\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2+2\overrightarrow{OG}(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})$$\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2$ $\begin{cases}\overrightarrow{OA}=\frac{1}{2}\overrightarrow{GA} \\ \overrightarrow{OG}=\frac{1}{2}\overrightarrow{AG} \end{cases}$$\Rightarrow k^2=6MO^2+\frac{3}{2}AG^2$$\Leftrightarrow MO^2=\frac{1}{6}(k^2-\frac{3}{2}AG^2)$

	1	tạo mới		Trả lời 10-03-13 05:33 PM gunbk92 1
a/$3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}$ =$3\overrightarrow{OA}+\overrightarrow{OG}+\overrightarrow{GB}+\overrightarrow{OG}+\overrightarrow{GC}+\overrightarrow{OG}+\overrightarrow{GD}$ =$3(\overrightarrow{OA}+\overrightarrow{OG})+(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})=0$(đpcm)b/$3MA^2+MB^2+MC^2+MD^2$$=3(\overrightarrow{MO}+\overrightarrow{OA})^2+(\overrightarrow{MO}+\overrightarrow{OB})^2+(\overrightarrow{MO}+\overrightarrow{OC})^2+(\overrightarrow{MO}+\overrightarrow{OD})^2$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2+2\overrightarrow{MO}(3\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD})$ $=6MO^2+3OA^2+OB^2+OC^2+OD^2$ (đpcm)c/ $k^2=3MA^2+MB^2+MC^2+MD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+OB^2+OC^2+OD^2$$\Leftrightarrow k^2=6MO^2+3OA^2+(\overrightarrow{OG}+\overrightarrow{GB})^2+(\overrightarrow{OG}+\overrightarrow{GC})^2+(\overrightarrow{OG}+\overrightarrow{GD})^2$ $\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2+2\overrightarrow{OG}(\overrightarrow{GB}+\overrightarrow{GC}+\overrightarrow{GD})$$\Leftrightarrow k^2=6MO^2+3OA^2+3OG^2$ $\begin{cases}\overrightarrow{OA}=\frac{1}{2}\overrightarrow{GA} \\ \overrightarrow{OG}=\frac{1}{2}\overrightarrow{AG} \end{cases}$$\Rightarrow k^2=6MO^2+\frac{3}{2}AG^2$$\Leftrightarrow \overrightarrow{MO}=\frac{1}{6}(k^2-\frac{3}{2}AG^2)$

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