Question Number 48204 by ajfour last updated on 20/Nov/18
$$\mathrm{2}\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}\right)\left({y}^{\mathrm{4}} −\mathrm{3}{y}^{\mathrm{2}} +\mathrm{4}\right)=\mathrm{7} \\ $$$${Find}\:\left({x},{y}\right)\:. \\ $$
Answered by ajfour last updated on 20/Nov/18
![2[(x^2 −1)^2 +2][(y^2 −(3/2))^2 +(7/4)]= 7 ⇒ x = ±1, y = ±(√(3/2)) four points.](https://www.tinkutara.com/question/Q48206.png)
$$\mathrm{2}\left[\left({x}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2}\right]\left[\left({y}^{\mathrm{2}} −\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{7}}{\mathrm{4}}\right]=\:\mathrm{7} \\ $$$$\Rightarrow\:\:{x}\:=\:\pm\mathrm{1},\:\:{y}\:=\:\pm\sqrt{\frac{\mathrm{3}}{\mathrm{2}}} \\ $$$$\:\:\:\:\:{four}\:{points}. \\ $$