Question

Розв'яжіть систему рівнянь.

Answer 1

$\displaystyle\bf\\\left \{ {{x^{2} y^{2}-x y^{3} =30 } \atop {x^{3} y-x^{2} y^{2}=180 }} \right.\\\\\\:\left \{ {{x^{2} y\cdot(x-y)=180} \atop {x y^{2} \cdot(x-y)=30}} \right. \\-----------\\\frac{x}{y} =6\\\\x=6y\\\\(6y)^{2}\cdot y^{2} -6y\cdot y^{3} =30\\\\36y^{4} -6y^{4} =30\\\\30y^{4}=30\\\\y^{4} =1\\\\y_{1} =1 \ \ \ \Rightarrow \ \ \ x_{1} =6\cdot 1=6\\\\y_{2} =-1 \ \ \ \Rightarrow \ \ \ x_{2} =6\cdot (-1)=-6\\\\\\Otvet \ : \ (6 \ ; \ 1) \ , \ (-6 \ ; \ -1)$