حل {l}{3n-9m+2*2m-3mn=5}{o=5m-7n}{p=o}{q=p}{r=q}{s=r}{text{Solvefor}ttext{where}}{t=s}

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

برای n،m،o،p،q،r،s،t حل کنید (complex solution)

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

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

برای n،m،o،p،q،r،s،t حل کنید

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