แก้โจทย์ {l}{1/a^2+1/b^2=1}{a/4x^2+21/36a^2=1}

$$\left\{ \begin{array} { l } { \frac { 1 } { a ^ { 2 } } + \frac { 1 } { b ^ { 2 } } = 1 } \\ { \frac { a } { 4 x ^ { 2 } } + \frac { 21 } { 36 a ^ { 2 } } = 1 } \end{array} \right.$$

หาค่า x (complex solution)

$$x=-\sqrt{3}i\left(7-12a^{2}\right)^{-\frac{1}{2}}a^{\frac{3}{2}}$$

$$x=\sqrt{3}i\left(7-12a^{2}\right)^{-\frac{1}{2}}a^{\frac{3}{2}}\text{, }b\neq \frac{\sqrt{35}i}{5}\text{ and }b\neq -\frac{\sqrt{35}i}{5}\text{ and }\left(a=i\left(1-b^{2}\right)^{-\frac{1}{2}}b\text{ or }a=-i\left(1-b^{2}\right)^{-\frac{1}{2}}b\right)\text{ and }b\neq 1\text{ and }b\neq -1\text{ and }b\neq 0$$

หาค่า x

$$x=\sqrt{-\frac{3a^{3}}{7-12a^{2}}}$$

$$x=-\sqrt{-\frac{3a^{3}}{7-12a^{2}}}\text{, }\left(\sqrt{-\frac{1}{1-b^{2}}}b>-\frac{\sqrt{21}}{6}\text{ and }a=\sqrt{-\frac{1}{1-b^{2}}}b\text{ and }b<-1\right)\text{ or }\left(\sqrt{-\frac{1}{1-b^{2}}}b<\frac{\sqrt{21}}{6}\text{ and }a=-\sqrt{-\frac{1}{1-b^{2}}}b\text{ and }b>1\right)\text{ or }\left(a=-\sqrt{-\frac{1}{1-b^{2}}}b\text{ and }\sqrt{-\frac{1}{1-b^{2}}}b<-\frac{\sqrt{21}}{6}\text{ and }b<-1\right)\text{ or }\left(a=\sqrt{-\frac{1}{1-b^{2}}}b\text{ and }\sqrt{-\frac{1}{1-b^{2}}}b>\frac{\sqrt{21}}{6}\text{ and }b>1\right)$$