Question Number 186124 by Rupesh123 last updated on 01/Feb/23
Commented by MJS_new last updated on 01/Feb/23
$$\mathrm{3}^{\mathrm{2}} +\mathrm{4}^{\mathrm{2}} =\mathrm{25}\:\Rightarrow\:\mathrm{I}\:\mathrm{guess}\:{y}\in\left\{\mathrm{3},\:\mathrm{4}\right\} \\ $$$$\mathrm{with}\:{y}=\mathrm{4}\:\Rightarrow\:{x}=\frac{\mathrm{215}}{\mathrm{106}}\pm\frac{\mathrm{27}\sqrt{\mathrm{17}}}{\mathrm{106}}\mathrm{i} \\ $$$$\Rightarrow\:{y}=\mathrm{3} \\ $$
Answered by MJS_new last updated on 01/Feb/23
$${x}=\frac{\mathrm{12}}{\mathrm{5}}\:{y}=\mathrm{3}\:{z}=\frac{\mathrm{18}}{\mathrm{5}} \\ $$$${xyz}=\frac{\mathrm{648}}{\mathrm{25}} \\ $$