Question

Помогите решить, пожалуйста)

Answer 1

$....... \left \{ {{x^2(x^2+y^2)=20} \atop {y^2(y^2+x^2)=5}} \right. \; \left \{ {{x^2+y^2=\frac{20}{x^2}} \atop {y^2\cdot \frac{20}{x^2}=5}} \right. \; \Rightarrow \frac{y^2}{x^2}=\frac{5}{20}\; ,\frac{x^2}{y^2}=\frac{20}{5}=4\; ,\; (\frac{x}{y})^2=4\\\\ \left \{ {{\frac{x}{y}=\pm 2} \atop {x^4+x^2y^2=20}} \right. \; \left \{ {{x=\pm 2y} \atop {16y^4+4y^4=20}} \right. \; \left \{ {{x=\pm 2y} \atop {y^4=1}} \right. \; \left \{ {{x=\pm 2y} \atop {y=\pm 1}} \right.$

$\left \{ {{x=\pm 2} \atop {y=\pm 1}} \right. \\\\Otvet:\; (2,-1)\; ;(-2,-1)\; ;(2,1)\; ;(-2,1)\; .$