Question Number 217066 by ArshadS last updated on 28/Feb/25
$${Find}\:{all}\:{integer}\:{x},{y}\:{such}\:{that} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{100} \\ $$
Answered by mehdee7396 last updated on 28/Feb/25
$$\left({x}−{y}\right)\left({x}+{y}\right)=\mathrm{2}×\mathrm{50}=\mathrm{10}×\mathrm{10} \\ $$$${x}−{y}=\mathrm{2}\:\&\:{x}+{y}=\mathrm{50}\Rightarrow{x}=\mathrm{26}\:\&\:{y}=\mathrm{24} \\ $$$${x}−{y}=\mathrm{10}\:\&\:{x}+{y}=\mathrm{10}\Rightarrow{x}=\mathrm{10}\:\&\:{y}=\mathrm{0} \\ $$$$ \\ $$
Commented by ArshadS last updated on 28/Feb/25
$${You}\:{considered}\:{only}\:{successful}\:{cases}. \\ $$$${Thanks}\:{anyway}! \\ $$