解決S=h^2/5/w^2*r |Microsoft數學求解器

$$S = \frac { h ^ { 2 } } { 5 } / w ^ { 2 } \cdot r$$

解 h (復數求解)

$$\left\{\begin{matrix}h=-r^{-\frac{1}{2}}\sqrt{5S}w\text{; }h=r^{-\frac{1}{2}}\sqrt{5S}w\text{, }&r\neq 0\text{ and }w\neq 0\\h\in \mathrm{C}\text{, }&S=0\text{ and }r=0\text{ and }w\neq 0\end{matrix}\right.$$

解 S

$$S=\frac{\left(\frac{h}{w}\right)^{2}r}{5}$$

$$w\neq 0$$

解 h

$$\left\{\begin{matrix}h=\sqrt{\frac{5S}{r}}w\text{; }h=-\sqrt{\frac{5S}{r}}w\text{, }&\left(S\geq 0\text{ and }r>0\text{ and }w\neq 0\right)\text{ or }\left(S\leq 0\text{ and }r<0\text{ and }w\neq 0\right)\\h\in \mathrm{R}\text{, }&S=0\text{ and }r=0\text{ and }w\neq 0\end{matrix}\right.$$