解決S=(w^2*r_{1})/(h^2/r_{0}) |Microsoft數學求解器

$$S = ( w ^ { 2 } \cdot r _ { 1 } ) / ( \frac { h ^ { 2 } } { r _ { 0 } } )$$

解 h (復數求解)

$$\left\{\begin{matrix}h=-S^{-\frac{1}{2}}\sqrt{r_{0}}\sqrt{r_{1}}w\text{; }h=S^{-\frac{1}{2}}\sqrt{r_{0}}\sqrt{r_{1}}w\text{, }&r_{0}\neq 0\text{ and }r_{1}\neq 0\text{ and }w\neq 0\text{ and }S\neq 0\\h\neq 0\text{, }&\left(r_{1}=0\text{ or }w=0\right)\text{ and }S=0\text{ and }r_{0}\neq 0\end{matrix}\right.$$

解 S

$$S=\left(\frac{w}{h}\right)^{2}r_{0}r_{1}$$

$$h\neq 0\text{ and }r_{0}\neq 0$$

解 h

$$\left\{\begin{matrix}h=w\sqrt{\frac{r_{0}r_{1}}{S}}\text{; }h=-w\sqrt{\frac{r_{0}r_{1}}{S}}\text{, }&\left(w\neq 0\text{ and }S>0\text{ and }r_{1}<0\text{ and }r_{0}<0\right)\text{ or }\left(w\neq 0\text{ and }S<0\text{ and }r_{0}<0\text{ and }r_{1}>0\right)\text{ or }\left(w\neq 0\text{ and }S<0\text{ and }r_{1}<0\text{ and }r_{0}>0\right)\text{ or }\left(w\neq 0\text{ and }S>0\text{ and }r_{0}>0\text{ and }r_{1}>0\right)\\h\neq 0\text{, }&\left(r_{1}=0\text{ or }w=0\right)\text{ and }S=0\text{ and }r_{0}\neq 0\end{matrix}\right.$$