Question Number 61744 by Cheyboy last updated on 08/Jun/19
$$\mathrm{3}{xy}^{\mathrm{2}} +{x}^{\mathrm{3}} =\mathrm{9}\:−−−−−\left(\mathrm{1}\right) \\ $$$$\mathrm{3}{x}^{\mathrm{2}} {y}+{y}^{\mathrm{3}} =\mathrm{18}−−−−\left(\mathrm{2}\right) \\ $$$${Find}\:{x}\:{and}\:{y} \\ $$
Commented by Cheyboy last updated on 08/Jun/19
$${thank}\:{Godbless}\:{you} \\ $$
Commented by Cheyboy last updated on 08/Jun/19
$${sir}\:{how}\:{did}\:{the}\:\mathrm{3}\:{disapper} \\ $$
Commented by Prithwish sen last updated on 08/Jun/19
$$\mathrm{Adding}\:\left(\mathrm{1}\right)\:\mathrm{and}\:\left(\mathrm{2}\right) \\ $$$$\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{3}} =\mathrm{27} \\ $$$$\therefore\:\mathrm{x}+\mathrm{y}\:=\mathrm{3}.......\left(\mathrm{3}\right) \\ $$$$\mathrm{Substracting}\:\left(\mathrm{2}\right)\:\mathrm{from}\:\left(\mathrm{1}\right) \\ $$$$\left(\mathrm{x}−\mathrm{y}\right)^{\mathrm{3}} =−\mathrm{9} \\ $$$$\therefore\:\mathrm{x}−\mathrm{y}\:=−\mathrm{9}^{\frac{\mathrm{1}}{\mathrm{3}}} .......\left(\mathrm{4}\right) \\ $$$$\mathrm{Adding}\:\left(\mathrm{3}\right)\:\mathrm{and}\:\left(\mathrm{4}\right) \\ $$$$\mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{3}−\mathrm{9}^{\frac{\mathrm{1}}{\mathrm{3}}} \right) \\ $$$$\mathrm{Substracting}\:\left(\mathrm{4}\right)\mathrm{from}\:\left(\mathrm{3}\right) \\ $$$$\mathrm{y}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{3}+\mathrm{9}^{\frac{\mathrm{1}}{\mathrm{3}}} \right) \\ $$$$ \\ $$
Commented by gunawan last updated on 08/Jun/19
$$\mathrm{nice}\:\mathrm{solution} \\ $$
Commented by Prithwish sen last updated on 08/Jun/19
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir}. \\ $$
Commented by Rasheed.Sindhi last updated on 08/Jun/19
$$\mathfrak{e}^{\mathrm{x}} \mathfrak{cellent}! \\ $$
Commented by Prithwish sen last updated on 08/Jun/19
$$\mathrm{thank}\:\mathrm{you} \\ $$