Lutasin ang H=4xsqrt{m^2+n^2}

$$H = 4x \sqrt{ { m }^{ 2 } + { n }^{ 2 } }$$

I-solve ang m (complex solution)

$$\left\{\begin{matrix}m=-\frac{\sqrt{-16n^{2}+\left(\frac{H}{x}\right)^{2}}}{4}\text{; }m=\frac{\sqrt{-16n^{2}+\left(\frac{H}{x}\right)^{2}}}{4}\text{, }&x\neq 0\text{ and }\left(|arg(\sqrt{\left(\frac{H}{x}\right)^{2}}x)-arg(H)|<\pi \text{ or }H=0\right)\\m\in \mathrm{C}\text{, }&H=0\text{ and }x=0\end{matrix}\right.$$

I-solve ang H

$$H=4x\sqrt{m^{2}+n^{2}}$$

I-solve ang m

$$\left\{\begin{matrix}m=\frac{\sqrt{H^{2}-16\left(nx\right)^{2}}}{4|x|}\text{; }m=-\frac{\sqrt{H^{2}-16\left(nx\right)^{2}}}{4|x|}\text{, }&\left(H\geq 4x|n|\text{ and }H\geq 0\text{ and }x>0\right)\text{ or }\left(H\leq 4x|n|\text{ and }H\leq 0\text{ and }x<0\right)\\m\in \mathrm{R}\text{, }&H=0\text{ and }x=0\end{matrix}\right.$$