Question Number 213751 by hardmath last updated on 15/Nov/24
$$\mathrm{m}\:;\:\mathrm{n}\:\in\:\mathbb{Z}_{+} \\ $$$$\mathrm{2m}^{\mathrm{2}} \:+\:\mathrm{n}^{\mathrm{2}} \:−\:\mathrm{mn}\:=\:\mathrm{54} \\ $$$$ \\ $$$$\mathrm{1}.\:\left(\mathrm{m};\mathrm{n}\right)=? \\ $$$$\mathrm{2}.\:\left(\mathrm{m};\mathrm{n}\right)=? \\ $$$$……………. \\ $$
Commented by hardmath last updated on 15/Nov/24
$$\left.\mathrm{a}\left.\right)\left.\:\left.\mathrm{1}\left.\:\:\:\:\:\mathrm{b}\right)\:\mathrm{2}\:\:\:\:\:\mathrm{c}\right)\:\mathrm{3}\:\:\:\:\:\mathrm{d}\right)\:\mathrm{4}\:\:\:\:\:\mathrm{e}\right)\:\mathrm{5} \\ $$
Answered by Ghisom last updated on 15/Nov/24
$$\mathrm{no}\:\mathrm{solution}\:\mathrm{for}\:{m},\:{n}\:\in\mathbb{Z}^{+} \\ $$
Commented by hardmath last updated on 15/Nov/24
$$\mathrm{m};\mathrm{n}\in\mathbb{N} \\ $$