Question

$$\sqrt{ax}=b$$

Solve for a

$\left\{\begin{matrix}a=\frac{b^{2}}{x}\text{, }&b\geq 0\text{ and }x\neq 0\\a\in \mathrm{R}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$

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Solve for a (complex solution)

$\left\{\begin{matrix}a=\frac{b^{2}}{x}\text{, }&x\neq 0\text{ and }\left(b=0\text{ or }arg(b)<\pi \right)\\a\in \mathrm{C}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$

Solve for b (complex solution)

$b=\sqrt{ax}$

Solve for b

$b=\sqrt{ax}$
$\left(x\geq 0\text{ and }a\geq 0\right)\text{ or }\left(a\leq 0\text{ and }x\leq 0\right)$