Question Number 10045 by konen last updated on 21/Jan/17
$$\mathrm{y}\rangle\mathrm{0} \\ $$$$\frac{\mathrm{3x}^{\mathrm{2}} −\mathrm{3xy}+\mathrm{y}^{\mathrm{2}} }{\mathrm{y}^{\mathrm{2}} }=\mathrm{7}\:\Rightarrow\mathrm{max}\left(\mathrm{x}\right)=? \\ $$
Answered by mrW1 last updated on 21/Jan/17
$$\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3}{xy}+{y}^{\mathrm{2}} =\mathrm{7}{y}^{\mathrm{2}} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3}{xy}−\mathrm{6}{y}^{\mathrm{2}} =\mathrm{0} \\ $$$${x}^{\mathrm{2}} −{yx}−\mathrm{2}{y}^{\mathrm{2}} =\mathrm{0} \\ $$$$\left({x}−\mathrm{2}{y}\right)\left({x}+{y}\right)=\mathrm{0} \\ $$$${x}=\left(\mathrm{2}{y},−{y}\right) \\ $$$$\Rightarrow{max}\left({x}\right)=\mathrm{2}{y} \\ $$