Question Number 62234 by aliesam last updated on 18/Jun/19
Answered by tanmay last updated on 18/Jun/19
$$\mathrm{9}\left({x}+{y}\right)=\left({x}+{y}\right)\left({x}^{\mathrm{2}} −{xy}+{y}^{\mathrm{2}} \right) \\ $$$$\left({x}+{y}\right)\left(\mathrm{9}−{x}^{\mathrm{2}} +{xy}−{y}^{\mathrm{2}} \right)=\mathrm{0} \\ $$$${eithdr}\:{x}+{y}=\mathrm{0}\:\:\:{or}\:{x}^{\mathrm{2}} −{xy}+{y}^{\mathrm{2}} =\mathrm{9} \\ $$$${x}=−{y} \\ $$$${y}^{\mathrm{3}} =−\mathrm{2}{y}+\mathrm{7}{y} \\ $$$${y}\left({y}^{\mathrm{2}} −\mathrm{5}\right)=\mathrm{0}\:\:{either}\:{y}=\mathrm{0}\:\:{or}\:{y}^{\mathrm{2}} =\mathrm{5} \\ $$$${so}\:\:{x}=\mathrm{0}\:\:\:{y}=\mathrm{0}\:\:\:{or} \\ $$$${x}=−\sqrt{\:\mathrm{5}}\:\:{y}=\sqrt{\mathrm{5}}\:\:\:{and}\:\:{x}=\sqrt{\mathrm{5}}\:\:\:{y}=−\sqrt{\mathrm{5}}\:\: \\ $$$$ \\ $$$$\mathrm{5}\left({x}−{y}\right)=\left({x}−{y}\right)\left({x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} \right) \\ $$$$\left({x}−{y}\right)=\mathrm{0}\:\:{or}\:{x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} =\mathrm{5} \\ $$$${x}^{\mathrm{3}} =\mathrm{7}{x}+\mathrm{2}{x} \\ $$$${x}\left({x}^{\mathrm{2}} −\mathrm{9}\right)=\mathrm{0}\:\:\:\:\:{whenx}^{\mathrm{2}} −\mathrm{9}=\mathrm{0}\:\:\:\:{x}=\pm\mathrm{3}\:\:\:{so}\:{y}=\pm\mathrm{3} \\ $$