다음을 풀어보세요: {l}{3n-9m+2*2m-3mn=5}{o=5m-7n}{p=o}{q=p}{text{Solvefor}rtext{where}}{r=q}

$$\left. \begin{array} { l } { 3 n - 9 m + 2 \cdot 2 m - 3 m n = 5 }\\ { o = 5 m - 7 n }\\ { p = o }\\ { q = p }\\ { \text{Solve for } r \text{ where} } \\ { r = q } \end{array} \right.$$

n, m, o, p, q, r에 대한 해 (complex solution)

$$r\in \mathrm{C}\text{, }n=\frac{-\sqrt{9r^{2}-300r-1700}-3r-20}{42}\text{, }m=\frac{-\sqrt{9r^{2}-300r-1700}+3r-20}{30}\text{, }o=r\text{, }p=r\text{, }q=r$$

$$r\in \mathrm{C}\text{, }n=\frac{5\left(\sqrt{9r^{2}-300r-1700}+3r+10\right)}{3\left(-\sqrt{9r^{2}-300r-1700}-3r+50\right)}\text{, }m=\frac{\sqrt{9r^{2}-300r-1700}+3r-20}{30}\text{, }o=r\text{, }p=r\text{, }q=r$$

n, m, o, p, q, r에 대한 해

$$r\in (-\infty,\frac{10(5-\sqrt{42})}{3}]\cup [\frac{10(\sqrt{42}+5)}{3},\infty)\text{, }n=\frac{-\sqrt{9r^{2}-300r-1700}-3r-20}{42}\text{, }m=\frac{-\sqrt{9r^{2}-300r-1700}+3r-20}{30}\text{, }o=r\text{, }p=r\text{, }q=r\text{; }r\in (-\infty,\frac{10(5-\sqrt{42})}{3}]\cup [\frac{10(\sqrt{42}+5)}{3},\infty)\text{, }n=\frac{5(\sqrt{9r^{2}-300r-1700}+3r+10)}{3(-\sqrt{9r^{2}-300r-1700}-3r+50)}\text{, }m=\frac{\sqrt{9r^{2}-300r-1700}+3r-20}{30}\text{, }o=r\text{, }p=r\text{, }q=r$$