다음을 풀어보세요: y=|x|(x-4)-x-mcosy=

$$y = | x | ( x - 4 ) - x - m \cos y =$$

m에 대한 해

$$\left\{\begin{matrix}m=\frac{x|x|-4|x|-x-y}{\cos(y)}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }y=\pi n_{1}+\frac{\pi }{2}\\m\in \mathrm{R}\text{, }&y=|x|\left(x-4\right)-x\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }n_{1}=-\frac{-2x|x|+8|x|+2x+\pi }{2\pi }\end{matrix}\right.$$

x에 대한 해

$$\left\{\begin{matrix}x=\frac{-\sqrt{4m\cos(y)+4y+25}+5}{2}\text{, }&\frac{4m\cos(y)+4y+25}{4}=0\text{ or }\left(m\geq -\frac{y}{\cos(y)}\text{ and }m\leq -\frac{4y+25}{4\cos(y)}\text{ and }\exists n_{4}\in \mathrm{Z}\text{ : }\left(y>\frac{\pi \left(4n_{4}+1\right)}{2}\text{ and }y<\frac{\pi \left(4n_{4}+3\right)}{2}\right)\right)\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }y=\frac{\pi \left(2n_{1}+1\right)}{2}\text{ or }\left(m\geq -\frac{4y+25}{4\cos(y)}\text{ and }m\leq -\frac{y}{\cos(y)}\text{ and }\exists n_{3}\in \mathrm{Z}\text{ : }\left(y>\frac{\pi \left(4n_{3}+3\right)}{2}\text{ and }y<\frac{\pi \left(4n_{3}+5\right)}{2}\right)\right)\\x=\frac{\sqrt{4m\cos(y)+4y+25}+5}{2}\text{, }&\left(\exists n_{5}\in \mathrm{Z}\text{ : }\left(y\geq \frac{\pi \left(4n_{5}+3\right)}{2}\text{ and }y\leq \frac{\pi \left(4n_{5}+5\right)}{2}\right)\text{ or }m\leq -\frac{4y+25}{4\cos(y)}\right)\text{ and }\left(\exists n_{1}\in \mathrm{Z}\text{ : }\left(y\geq \frac{\pi \left(4n_{1}+1\right)}{2}\text{ and }y\leq \frac{\pi \left(4n_{1}+3\right)}{2}\right)\text{ or }m\geq -\frac{4y+25}{4\cos(y)}\right)\\x=\frac{-\sqrt{-4m\cos(y)-4y+9}+3}{2}\text{, }&\left(m\geq -\frac{y}{\cos(y)}\text{ and }\exists n_{4}\in \mathrm{Z}\text{ : }\left(y>\frac{\pi \left(4n_{4}+1\right)}{2}\text{ and }y<\frac{\pi \left(4n_{4}+3\right)}{2}\right)\right)\text{ or }\left(m\leq -\frac{y}{\cos(y)}\text{ and }\exists n_{3}\in \mathrm{Z}\text{ : }\left(y>\frac{\pi \left(4n_{3}+3\right)}{2}\text{ and }y<\frac{\pi \left(4n_{3}+5\right)}{2}\right)\right)\text{ or }\left(m<\frac{9-4y}{4\cos(y)}\text{ and }\exists n_{6}\in \mathrm{Z}\text{ : }\left(y>\frac{\pi \left(2n_{6}+1\right)}{2}\text{ and }y<\frac{\pi \left(2n_{6}+3\right)}{2}\right)\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }y=\frac{\pi \left(2n_{1}+1\right)}{2}\text{ and }\exists n_{4}\in \mathrm{Z}\text{ : }\left(y>\frac{\pi \left(4n_{4}+1\right)}{2}\text{ and }y<\frac{\pi \left(4n_{4}+3\right)}{2}\right)\text{ and }\exists n_{2}\in \mathrm{Z}\text{ : }\left(y\geq \frac{\pi \left(4n_{2}+3\right)}{2}\text{ and }y\leq \frac{\pi \left(4n_{2}+5\right)}{2}\right)\right)\end{matrix}\right.$$