{l}{x_{1}=2sqrt{-Q}cos(θ/3)-frac{a_{1}}{3}}{x_{2}=2sqrt{-Q}cos(θ+2pi/3)-frac{a_{1}}{3}}{x_{3}=2sqrt{-Q}cos(θ+4pi/3)-frac{a_{1}}{3}} を解きます| Microsoft 数学ソルバー

$$\left\{ \begin{array} { l } { x _ { 1 } = 2 \sqrt { - Q } \cos ( \frac { \theta } { 3 } ) - \frac { a _ { 1 } } { 3 } } \\ { x _ { 2 } = 2 \sqrt { - Q } \cos ( \frac { \theta + 2 \pi } { 3 } ) - \frac { a _ { 1 } } { 3 } } \\ { x _ { 3 } = 2 \sqrt { - Q } \cos ( \frac { \theta + 4 \pi } { 3 } ) - \frac { a _ { 1 } } { 3 } } \end{array} \right.$$

x_1,x_2,x_3 を解く (複素数の解)

$$x_{1}=\frac{6\sqrt{-Q}\cos(\frac{\theta }{3})-a_{1}}{3}$$

$$x_{2}=\sqrt{-Q}e^{\frac{i\theta +2\pi i}{3}}+\sqrt{-Q}e^{\frac{-i\theta -2\pi i}{3}}-\frac{a_{1}}{3}$$

$$x_{3}=\sqrt{-Q}e^{\frac{i\theta +4\pi i}{3}}+\sqrt{-Q}e^{\frac{-i\theta -4\pi i}{3}}-\frac{a_{1}}{3}$$

x_1,x_2,x_3 を解く

$$x_{1}=\frac{6\sqrt{-Q}\cos(\frac{\theta }{3})-a_{1}}{3}$$

$$x_{2}=\frac{6\sqrt{-Q}\cos(\frac{\theta +2\pi }{3})-a_{1}}{3}$$

$$x_{3}=\frac{6\sqrt{-Q}\cos(\frac{\theta +4\pi }{3})-a_{1}}{3}$$

$$Q\leq 0$$