Question Number 197623 by hardmath last updated on 24/Sep/23
$$\mathrm{x},\mathrm{y}\in\mathbb{N} \\ $$$$\mathrm{162}\:\centerdot\:\mathrm{x}^{\mathrm{2}} \:=\:\mathrm{y}^{\mathrm{3}} \\ $$$$\mathrm{min}\left(\mathrm{x}+\mathrm{y}\right)=? \\ $$
Commented by SANOGO last updated on 25/Sep/23
merci bien monsieur
Answered by Frix last updated on 24/Sep/23
$$\mathrm{162}=\mathrm{2}×\mathrm{3}^{\mathrm{4}} \\ $$$$\left(\mathrm{2}×\mathrm{3}^{\mathrm{4}} \right)×\left(\mathrm{2}×\mathrm{3}\right)^{\mathrm{2}} =\mathrm{2}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{6}} =\left(\mathrm{2}×\mathrm{3}^{\mathrm{2}} \right)^{\mathrm{3}} \\ $$$${x}=\mathrm{6}\wedge{y}=\mathrm{18} \\ $$$${x}+{y}=\mathrm{24} \\ $$