Solve for P (complex solution)
P=\frac{\sqrt{3km}}{2T^{2}}
T\neq 0
Solve for T (complex solution)
\left\{\begin{matrix}T=-\frac{\sqrt{2}P^{-\frac{1}{2}}\sqrt[4]{3km}}{2}\text{; }T=\frac{\sqrt{2}P^{-\frac{1}{2}}\sqrt[4]{3km}}{2}\text{, }&k\neq 0\text{ and }m\neq 0\text{ and }P\neq 0\\T\neq 0\text{, }&\left(m=0\text{ or }k=0\right)\text{ and }P=0\end{matrix}\right.
Solve for P
P=\frac{\sqrt{3km}}{2T^{2}}
T\neq 0\text{ and }\left(k\geq 0\text{ or }m\leq 0\right)\text{ and }\left(m\geq 0\text{ or }k\leq 0\right)
Solve for T
\left\{\begin{matrix}T=\frac{\sqrt{\frac{2}{P}}\sqrt[4]{3km}}{2}\text{; }T=-\frac{\sqrt{\frac{2}{P}}\sqrt[4]{3km}}{2}\text{, }&\left(P>0\text{ and }m<0\text{ and }k<0\right)\text{ or }\left(P>0\text{ and }k>0\text{ and }m>0\right)\\T\neq 0\text{, }&\left(m=0\text{ or }k=0\right)\text{ and }P=0\end{matrix}\right.
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