Question Number 21653 by Joel577 last updated on 30/Sep/17
$$\mathrm{Find}\:\mathrm{all}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{solutions}\:\left({x},{y}\right)\:\mathrm{that}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{7}{x}^{\mathrm{2}} \:−\:\mathrm{13}{xy}\:+\:\mathrm{7}{y}^{\mathrm{2}} }\:=\:\mid{x}\:−\:{y}\mid\:+\:\mathrm{1} \\ $$