Question Number 201854 by cortano12 last updated on 14/Dec/23
Commented by cortano12 last updated on 14/Dec/23
$$\:\:\begin{cases}{\mathrm{x}^{\mathrm{2}} −\mathrm{3y}^{\mathrm{2}} =\frac{\mathrm{17}}{\mathrm{x}}}\\{\mathrm{3x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} =\frac{\mathrm{23}}{\mathrm{y}}}\end{cases} \\ $$$$\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\:\sqrt[{\mathrm{m}}]{\mathrm{n}}\:,\:\mathrm{m},\mathrm{n}\:\in\mathbb{Z}^{+} \: \\ $$$$\:\:\mathrm{m}+\mathrm{n}\:=? \\ $$
Commented by Frix last updated on 14/Dec/23
$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\sqrt[{\mathrm{3}}]{\mathrm{17}^{\mathrm{2}} +\mathrm{23}^{\mathrm{2}} }=\sqrt[{\mathrm{3}}]{\mathrm{818}} \\ $$$$\mathrm{3}+\mathrm{818}=\mathrm{821} \\ $$
Commented by cortano12 last updated on 14/Dec/23
$$\mathrm{by}\:\mathrm{complex}\:\mathrm{number} \\ $$