{l}{y=b/kx+c}{y=bx^2-kx-c} を解きます| Microsoft 数学ソルバー

$$\left. \begin{array} { l } { y = \frac { b } { k } x + c } \\ { y = b x ^ { 2 } - k x - c } \end{array} \right.$$

x,y を解く (複素数の解)

$$\left\{\begin{matrix}x=\frac{k\sqrt{8bc+k^{2}+2b+\left(\frac{b}{k}\right)^{2}}+k^{2}+b}{2bk}\text{, }y=c+\frac{\sqrt{8bc+k^{2}+2b+\left(\frac{b}{k}\right)^{2}}}{2k}+\frac{1}{2}+\frac{b}{2k^{2}}\text{; }x=\frac{-k\sqrt{8bc+k^{2}+2b+\left(\frac{b}{k}\right)^{2}}+k^{2}+b}{2bk}\text{, }y=c-\frac{\sqrt{8bc+k^{2}+2b+\left(\frac{b}{k}\right)^{2}}}{2k}+\frac{1}{2}+\frac{b}{2k^{2}}\text{, }&b\neq 0\text{ and }k\neq 0\\x=-\frac{2c}{k}\text{, }y=c\text{, }&k\neq 0\text{ and }b=0\end{matrix}\right.$$