แก้โจทย์ {l}{D=1/3BC}{(AD)^2=7(AB)^2}

$$\left. \begin{array} { l } { D = \frac { 1 } { 3 } B C } \\ { ( A D ) ^ { 2 } = 7 ( A B ) ^ { 2 } } \end{array} \right.$$

หาค่า D, B, C, A (complex solution)

$$D=\sqrt{7}\left(Re(B)+iIm(B)\right)\text{, }B\in \mathrm{C}\text{, }C=3\sqrt{7}\approx 7.937253933\text{, }A\in \mathrm{C}$$

$$D=-\sqrt{7}\left(Re(B)+iIm(B)\right)\text{, }B\in \mathrm{C}\text{, }C=-3\sqrt{7}\approx -7.937253933\text{, }A\in \mathrm{C}$$

$$D=\frac{BC}{3}\text{, }B\in \mathrm{C}\text{, }C\in \mathrm{C}\text{, }A=0$$

$$D=0\text{, }B=0\text{, }C\in \mathrm{C}\text{, }A\in \mathrm{C}$$

หาค่า D, B, C, A

$$D=-\sqrt{7}B\text{, }B\in \mathrm{R}\text{, }C=-3\sqrt{7}\approx -7.937253933\text{, }A\in \mathrm{R}$$

$$D=\sqrt{7}B\text{, }B\in \mathrm{R}\text{, }C=3\sqrt{7}\approx 7.937253933\text{, }A\in \mathrm{R}$$

$$D=\frac{BC}{3}\text{, }B\in \mathrm{R}\text{, }C\in \mathrm{R}\text{, }A=0$$

$$D=0\text{, }B=0\text{, }C\in \mathrm{R}\setminus 3\sqrt{7},-3\sqrt{7}\text{, }A\in \mathrm{R}$$