Задача 67692 { xy - x/y = 6 { 3xy + 2x/y = 28 ...

61f121929726a16dff0f8e8e

19.12.2022 14:59:34

{ xy - x/y = 6
{ 3xy + 2x/y = 28

5f3ea7e3faf909182968ddd9

19.12.2022 17:53:21

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Замена переменной:

[m]xy=u[/m]

[m]\frac{x}{y}=v[/m]

[m]\left\{\begin {matrix}u-v=6\\3u+2v=28\end {matrix}\right.[/m]

Умножаем первое на 2:

[m]\left\{\begin {matrix}2u-2v=12\\3u+2v=28\end {matrix}\right.[/m]

Складываем
[m]\left\{\begin {matrix}u-v=6\\5u=40\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}8-v=6\\u=8\end {matrix}\right.[/m]


[m]\left\{\begin {matrix}v=2\\u=8\end {matrix}\right.[/m]


Обратный переход:
[m]\left\{\begin {matrix}xy=2\\\frac{x}{y}=8\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}(8y)\cdot y=2\\x=8y\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}y^2=4\\x=8y\end {matrix}\right.[/m]

[m]\left\{\begin {matrix}y= 2\\x= 16\end {matrix}\right.[/m] или [m]\left\{\begin {matrix}y=- 2\\x= -16\end {matrix}\right.[/m]