Задача 55172 Найти решения систем уравнений { x^3 -...

5f9bb4ba6feaba08a85e0062

30.10.2020 09:40:05

Найти решения систем уравнений

{ x^3 - y^3 = 19(x - y)
{ x^3 + y^3 = 7(x + y)

5f3ea7e3faf909182968ddd9

30.10.2020 11:36:16

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[m]x^3-y^3=(x-y)\cdot (x^2+xy+y^2)[/m]

[m]x^3+y^3=(x+y)\cdot (x^2-xy+y^2)[/m]


[m]\left\{\begin{matrix}
(x-y)\cdot (x^2+xy+y^2)=19(x-y)\\ (x+y)\cdot (x^2-xy+y^2)=7(x+y)\end{matrix}\right.[/m]

[m]\left\{\begin{matrix}
(x-y)\cdot (x^2+xy+y^2)-19(x-y)=0\\ (x+y)\cdot (x^2-xy+y^2)-7(x+y)=0\end{matrix}\right.[/m]


[m]\left\{\begin{matrix}
(x-y)\cdot (x^2+xy+y^2-19)=0\\ (x+y)\cdot (x^2-xy+y^2-7)=0\end{matrix}\right.[/m]


[m]\left\{\begin{matrix}
x-y=0\\x+y=0\end{matrix}\right.[/m][m]\left\{\begin{matrix}
x-y=0\\ x^2-xy+y^2-7=0\end{matrix}\right.[/m][m]\left\{\begin{matrix}
x^2+xy+y^2-19=0\\ x+y=0\end{matrix}\right.[/m][m]\left\{\begin{matrix}
x^2+xy+y^2-19=0\\ x^2-xy+y^2-7=0\end{matrix}\right.[/m]